ornl-tm-2815

. . .

,- - - ! . # OAK RIDGE NATIONAL LABORATORY

operated by UNION CARBIDE CORPORATION NUCLEAR DIVISION

1 .

L. % 4

’Ilu ..

” . I for the ‘r L- U. S. ATOMIC E N E R G Y COMMISSION

-.

t-- L ORNL - TM - 2815

c

Y

c

COMPUTER PROGRAMS FOR MSBR HEAT EXCHANGERS

C. E, Bettis W, K . Crowley M. Siman-Tov H, A. Nelrns

T, W. Pickel

W. C. Stoddart

NOTICE This document contains information of a preliminary nature and was prepared primarily for internal use at the Oak Ridge National Laboratory. I t is subject to revision or correction and therefore does not represent a final report.

. .

4

8

This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that i t s use would not infringe privately owned rights.

I I

OAK RIDGE NATIONAL LABORATORY O P E R A T E D B Y

UNION CARBIDE CORPORATION N U C L E A R D I V I S I O N

POST OFFICE B O X X

OAK RIDGE, TENNESSEE 37830

June 24, 1971

To: Recipients o f Subject Report

Report N o . :- OR NL- TM-28 1 5 Class i f icat ion: Unclass i f ied

Author(s):_C_1 E. Bettis, W. K. Crowley, H. A . Nelms, T. W. Pickel

Subject : Computer Programs For MSBR Heat Exchangers

Request compl iance w i t h i nd i ca ted act ion:

Please a f f i x the a t tached corrected pages 6, 7, 58,62 , 63, 86,87,88,89, 117, 124, 125 to pages w i t h same numbers i n your copy(ies) of the subject report . They are prepared on gummed stock for your conven ience. Also prepared on gummed stock i s a cor rec t ion for the bot tom two l ines on page 9 o f the report .

Please ccrrect your copies promptly to avoid further errors.

the pr imary heat exchanger agree w i t h the da ta shown in Report N o . ORNL-4541. The corrected design data for

. . LaGoratory RecordsIDepartment Technica I Informat ion D i v i s i o n

6

Table 2.1, Design Data for MSBR Primary Heat Exchanger

Number required Rate of heat transfer per unit,

Mw Btu/hr

Hot fluid Entrance temperature, OF Exit temperature, OF Entrance pressure, psi Pressure drop across exchanger, psi Mass flow rate, lb/hr

Cold fluid Entrance temperature, O F Exit temperature, O F

Exit pressure, psi Pressure drop across exchanger, psi Mass flow rate, lb/hr

Material Number required Pitch, in. Outside diameter, in. Wall thickness, in. Length, ft

Tube sheet Materia 1 Thickness, in. Sheet-to-sheet distance, ft

Basis for area calculation

Tube-side conditions

She1 1- side conditions

Tube

Total heat transfer area, ft 2

Volume of fuel salt in tubes, ft3

Shell Mater tal Thickness, in. Inside diameter, in.

Central tube diameter, in.

Baffle Type Number Spacing, in.

Shell-and-tube one-pass vertical exchanger with disk and doughnut baffles

Four

556.5 1.9 109

Fuel salt 1300 1050 180 130 23.4 x IO6

Coolant salt 850 1150 34 115.7 17.8 x lo6

Hastelloy N 5803 0.75 0.375 0.035 24.4

Hastelloy N 4.75 23.2

13,916 Outside of tubes

71.9

Hastelloy N 0.5 67.6

20.0

Disk and doughnut 21 11.23

7

Table 2.1 (continued)

Disk o u t s i d e diameter, i n .

Doughnut i n s i d e diameter, i n .

Overall hea t r a n s f e r c o e f f i c i e n t , U,

Tube

Btu/hr. ft', O F

Maximum primary (P) stresses Calculated, p s i Allowable, p s i

(P + Q) s t r e s s e s Calculated, p s i Allowable, p s i

Calcu la ted , p s i Allowable, p s i

Maximum primary and secondary

Maximum peak (P + Q + F) stresses

54.20

45.3

784.8

68 3 4232

12,484 12,696

13,563 25,000

wave conf igu ra t ion .

upper po r t ion of t h e tube bundle.

t h i s region, t h e bent- tube po r t ion o f t h e bundle experiences e s s e n t i a l l y

paral le l flow and a r e l a t i v e l y lower h e a t t r a n s f e r performance.

The tubes are he ld i n p lace by w i r e l ac ing i n t h i s

Since b a f f l i n g i s not employed i n

Below t h e bent- tube reg ion of t h e bundle, evenly spaced doughnut-

shaped b a f f l e s are used t o hold t h e tubes i n p l ace and t o produce c r o s s

flow. The b a f f l e s spacings and cross-f low v e l o c i t i e s a r e designed t o min-

imize t h e p o s s i b i l i t y of flow-induced v i b r a t i o n . The tubes i n t h i s ba f -

f l e d reg ion of t h e hea t exchanger have a h e l i c a l i nden ta t ion knurled

i n t o t h e i r su r f ace t o enhance t h e f i l m hea t t r a n s f e r c o e f f i c i e n t s and

thereby reduce t h e f u e l s a l t inventory i n t h e exchanger. No enhancement

of t h i s n a t u r e w a s used i n the upper bent- tube region because of present

u n c e r t a i n t y about t h e r e l i a b i l i t y of tubes t h a t are both bent and

indented .

Bottom of page 9 : For completely tu rbu len t f low wi th Reynolds numbers g r e a t e r than

12,000,

1047 F O P M A T ( 3 1 W B E R G L I N M O D I F I C A T I O N FACTOR = ~ F 5 . 2 ) 1 0 4 8 FORMAT ( 1 HO, 2X , l H I 1 7 X 9 3 H T C I 9 9x9 3HTCO99X 9 3HC kT t 9 X 9

19x9 3HFWT9 8X r 4 H T W D T / / l l X , 1HF , 1 1 X , l H F , P l X , l H F 9 1 1 x 9

2

1

1 6 X 9 6HF EN S@3 9 7 x 9 3HHTO98X9 4HAHSOy 9X93HUOA , 8 X , 4 H H E A T / / 7 7 X 9

2 13HBTU/FR/SQFT/F ,13Xr6HBTU/HR/ / ( lX , 1 3 9 9 E 1 2 . 4 1 1

3 H T F I 9 9 X 93HT FO 9

1 H F 9 1 1 X T ~ H F ~ 11 X 9 1HF 9 1 l X 9 LHF / / (1 X 9 I3 97E12.4) 1 1049 F O R M A T ( l h C 9 ZX91HI ,9X ,2HV19 9 X 9 2 H V 2 r 9 X 9 2 H V 3 ,9X,3HVW1 ,9X,3HVW3 9

8 X 9 4 H P D S 0 9 8X ,4HPCTC/ /32X, 6HFT/SEC, 3 3 X , 7 H L B / S Q F T / / ( 1 X 9 I 3 9 7 F l 2 04) 1 1 0 5 G F O R M A T ( l H 0 9 2 X ,1HI ,5X,5HRENT0,7X95HPRNT0,7X1CHRENSO1 96X96HRENS02 ,

P O 5 1 FORMAT(27PGTUEE WALL AVERAGE TEMP. = t F 1 0 0 21 1 0 5 2 F O R M A T ( 2 8 W S h E L L S I D E AVERAGE TEMP. = 9 F lG.21 1 0 5 3 F O R M A T ( l H 0 , 3 4 k P STRESS A T TUBE OD AND TUBE ID = T 2 F l O o 2 9 1 x 9

1 0 5 4 FORMAT(LHC,36kP+Q STRESS AT TUBE 00 AND TUBE I D = 9

1 9 H ( L B / S Q I N ) / / 1 8 H ( S H O U L D NOT EXCEED,F lOo2,3H 1 )

1 2F 1 0 0 2 9 1 X ,9H( L B / S Q I N ) / / 1 8 H ( SHOULC NOT E X C E E D 9 F l C o 2 9

2 3 H 1 ) 1 0 5 5 FORMAT(PHC,38kP+Q+F STRESS A T TUBE OD AFID TUBE I D = 9

A ~ F ~ ~ o ~ ~ ~ X ~ ~ H ~ L B / S Q I N ~ / / ~ ~ H ~ S H @ U L D NOT E X C E E D 9 F l O o 2 , 2 3 H 1 )

C C READ I N A h C P R I N T OUT I N P U T DATA

KEY7= 1 V M 1 ( 1 1 50 V M 2 ( 1 1 = 0 . V M 3 ( 1 ) = 0 o V W O l ( l ) = C . v w 0 3 ( 1 ) = O . REN SO 1 ( 1 1 =C R E N S O Z ( l ) = O o R E N S 0 3 ( 1 ) = O o H S O l ( l ) = O o H S O Z ( P ) = O o H S 0 3 ( 1 ) = O m

C

MSBR 500 MSBR 510 MSBP 511 MSBR 512 MSBF 5 2 @ MSBP 5 2 2 MSBP 530 MSBR 531 MSBP 5 3 2 MSBR 54C MSBR 55C MSBR 5 6 C MSBR 561 MSBR 570 MSBR 5 7 1 MSBR 5 7 2 MSBR 5 8 0

MSBP 5 8 2 MSBR 650 MSBP 660

cn MSBR 5 8 1 00

MSBR 610 MSBR 620 MSBR 030 MSBR 640 MSBR 650 MSBR 660 MSBR 670 MSBR 680 MSBR 690 MSBR 700 MSBR 710 MSBR 720 MSBR 810

I F ( KEY 1 0 E Qo C 1 eSOI=G. 5 * ( BSL+BSH 1 C U R V E S = C o C 6 S 8 1 2 * A R C * EXPRAD+ 0 0 4 * ( k A 8 - R A 5 ) + o 2 5 * B S O I I T = 0 K F I N A L =O

9 1=1 H E F I = 1 0 H E F O = 1. TSUM=Co SSUM=Co THEATO = (3.0 TPDTO = G o 0 TPDSO = 000 T F O ( I ) = F T C ! T C I ( I 1 =C T C T I F =- 5 .O T I C =-5 0 CDTF=Oo FDTF=Oo BSO = B S G X B R L l = B S C / ( ( R A S - ( F A ~ - R A ~ ) / ~ O ) - ( R A ~ - R A ~ ) / ~ . ) 1 GBRL = G m 7 7 * B R L l * * ( - 0 1 3 8 ) AWO1 = BSC*LAh01 AW03 = B S C s L A h 0 3 AW1 = S Q R T ( A k @ l * A P O l )

AN3 = SQRT ( A h C 3 * A P @ 3 ) GSOI. = Q C / P W l GSO2 = QC/AW2 G S 0 3 = QC/AW3 BSO=CURV E S

KEY4=C 1 0 KEY5=C

AWZ = (AbOl+Ak03) /2 .

EQVBSG= CURVES+ 13.* ( C I A + D I A I 1

11 ATC = T C I ( 1 ) + (TIC/Z.O) C F T = ATC +CDTF*HSFCT

FFT=ATF-FCTF*kSFCT F I = I T U B L N ( I) = ( F I - l . ) * B S O I + C U R V E S

A T F = T F O ( I ) + l I F / 2 .

MSB 1 8 5 0 MSB 1 8 4 0 MSB 1870 MSB 1 8 8 C MSB 1890 MSBR 730 MSBk 740 MSB 1900 MSB 1910 MSB 1920 MSB 193C MSB 1940 MSB 1950 MSB 1960 MSB 1970 Y S B 1 9 8 C MSB 1993 MSB 2 0 0 0 MSB 2010 MSB 2 G 2 0 MSB 2030 MSB 2 0 4 C MSB 2 C 5 0 MSB 2 0 6 G M S E 2C70 MSE! 2 C 8 0 MSB 2090 MSB 2100 MSB 2110 MSE! 2120 MSB 2130 MSB 2140 MSB 2150 M S 0 2 1 6 0

MSB 2180

MSB 2 2 0 0 MSB 2 2 1 0

CVIS=Co212l*EXF(40320/(460o+ATCI 1 MSB 2 2 2 C MSB 2 2 3 0 MSB 2 2 4 0 MSB 2 2 5 0 MSB 2 2 6 0 MSB 2 2 7 0

F V I SW=Oo 2 637* EXP ( 736 2, / ( 460. + F F T 1 I MSB 2 2 8 C FDEN=2 34 S7-OoO 2 3 1 7 * A T F MSB 2 2 9 C

MSB 2 3 0 0 F SP H=O 3 2 4 MSB 2 3 1 0

MSB 2320 F V I SK= ( F V IS / F V I SW 1 * * O e 14 MSB 2330 D C V I S = D I A / C V I S MSB 2 3 4 0 CCGEN = 1 o / C C E N MSB 2 3 5 0

MSB 2 3 6 0 QCCDEN = QC*CCDEN C CALCULATE REYKOLS AND PRANDTL NUMBER TUBE S I D E MSB 2 5 5 0

MSB 2 3 8 0 RENT0 ( I ) = C I A I *GTO/ F V I S PRNTO ( I) = FV I S * F S P H / FCCN MSB 2 3 9 C I F ( K E N T B o E Q o l o A N D o R E N T C ( I) o G T 0 1 0 0 1 0 .AND. IoNE.1) MSB 2 4 0 0

l H E F I = l o + ( ( R E N T G ( I ) - l G O O o ) / 9 C C G o ) * * O o 5 MSB 2401 MSB 2410

1 ( D I A I * F D E N * 4 1 7 1 8 2 4 C O o 1 MSB 2411 MSB 2 6 4 0

C V I Sk=Go 2 1 Z l * E X P (403 2. / ( 4 6 0 o + C F T ) I C D E N = 1 4 1 3 7 - G o 0 2 4 6 6 s A T C CCON=Co24C C SP H=O 36 FVIS=O.26 3 7 * E X P ( 7 3 6 2 o / ( 4 6 0 o + A T F 1 I

FCON=0.70

V I S K = ( C L I S / C V I S W ) * * O o 1 4

PDTO( I ) = ( o ~ G 2 ~ + o 2 5 * ~ E N T O * * ( - o 3 2 ) I *EQVBSOsGTO**Z*HEFI /

C CALCULATE HEAT TRANSFER COEFF TUBE S I D E I F ( R E N T O ( I) o L T o 1 2 C C C o )GO T O 1 2 HTO ( I 1 =FCCN/C I A * o C 2 1 7 * ( R E N T O ( I ) * *08)* (PRNTC ( I ) * * o 3 3 3 3 1 * F V I S K * H E F I M S 6 2 4 3 0 GO TO 15 MSB 2440

1 2 I F ( R E N T O ( I ) o L T o 2 1 C C o ) GO TO 14 MSB 2 4 5 0 P3 HTO( I 1 = F C O N / C I A * o C 8 9 * ( R E N T O ( I ) * * .67895-141 .1172) * (PRNTO( I )

1*%3333l* FV ISK*HEF I*( l o + o 3 3 3 3 * ( D E A I / T U B L N ( I) )**06666) GO TO 15 MSB 2470

1 4 H T O ( 1 ) = F C C N / C I A ~ ( 4 ~ 3 6 + ~ 0 ~ 0 2 5 ~ R E N T O ( I ~ ~ P R N T @ ~ I ~ ~ D I A I / T U B L N ~ I 1 MSB 2 4 8 0 1 ) / ( l o + C o O 0 1 2 * R E N T O t I ) * P R N T C ( I ) * D I A I / T U B L N ( I ) 1 ) MSB 2481

15 I F ( I o E Q o 1 I G O TO 16 MSB 2 4 9 0 C CALCULATE F L O b ARFAS SHELL S I D E M S 0 2 4 8 0

MSB 2510 V W O 1 ( I 1 = QCCDEN/AWOI V W 0 3 ( I) = QCCDEN/AWC3 MSB 2 5 2 0 V M l ( 1 ) = GSOl*CCDEN MSB 2 5 3 0 V M 2 ( I ) = GS024CCDEN MSB 2 5 4 0 V M 3 ( I ) = GSG3WCDEN MSB 2550

QI W

Computer Output f o r Reference MSBR Primary Heat Exchanger

TOTAL HEAT TRANSFERED = 18SE2179840 ( B T U / H R ) ( 9 9 0 9 PERCENT)

M A S S FLOW K A T E OF COOLANT = 1759Gi36 . t L B / H R )

MASS FLOW R A T t OF F U E L = 2 3 4 5 4 3 2 G o ( L B / H R )

S H E L L - S I D E TOTAL FRESSURE CRCP = 115.75 ( L B / S Q I N ) ( 9907 PERCENT)

T U B E - S I D E T O T A L PRESSURE CROP = 129.32 ( L B / S Q I N ) ( 99.5 PERCENT)

N O M I N A L S H E L L R A D I U S = 2 0 8 1 t 2 ( F T )

U N I F O R M B A F F L E S P A C I N G = L o 5 3 8 6 ( F T I

TUBE F L U I D VOLUME C O N T A I N E C I N TUBES = 71.92 ( C U B I C F E E T )

TOTAL HEAT TRANSFER AREA BASED ON TUBE 0.D. = 1 3 9 1 6 0 3 2 ( S Q F T )

TOTAL NUMBER OF TUBES = 58030

TOTAL TUBE LENGTH = 24.43 ( F T )

HEAT EXCH. APPROX. LENGTI- = 2 1 0 2 2 ( F E E T )

S T R A I G H T S E C T I G N OF TUBE LENGTH = 20.26 ( F T )

R A D I U S O F THERMAL E X P A N S I O N CURVES = 0.86 ( F E E T )

B E R G L I N M O D I F I C A T I O N FACTOR = 0.79

TUBE WALL AVERAGE TEMP, = 1116.54

SHELL S I D E AVERAGE TEMP. = 10130 66

P STRESS AT TUBE OD AND TUBE I D = 6 8 3 0 4 2 646.47 ( L B / S Q I N )

SHOULD NOT EXCEED 4 2 3 2 . 2 3 1

P+Q STRESS AT TUBE OD A N C TUeE IC = 1 2 4 8 4 . 3 9 8890.97 ( L B / S Q I N I

SHOULD NOT EXCEED 1 2 6 9 6 0 7 C 1

P+Q+F STRESS A T TUBE OD AND TUBE IT; = 1 3 5 6 2 0 7 7 10981.55 ( L B I S Q I N )

SHOULD NOT EXCEED 2500C.CO 1

I T C I T C C CWT TF I TFO FWT

F F F F F F

1 0 . 1 1 5 0 E 04 0o1122E 04 C o 1 2 4 C E C 4 0 . 1 2 7 6 E 04 0.1300E 04 0 0 1 2 5 6 E 04 2 0 o 1 1 2 2 E 04 0 o 1 1 0 8 E G4 0 0 1 1 7 8 E C 4 0 0 1 2 6 5 E 04 0 0 1 2 7 6 E 04 0 0 1 2 2 3 E 04 3 0 o 1 1 0 8 E G 4 0 o 1 0 9 4 E 04 0 o 1 1 6 S E 04 0 0 1 2 5 4 E 04 0 o 1 2 6 5 E 04 O o l Z l O E 04 4 0 o 1 0 9 4 E G 4 0 o l C 8 1 E 04 0 o 1 1 5 2 E 04 O.1242E 04 0.1254E 04 O o 1 1 9 8 E G 4 5 0 o 1 0 8 1 E 04 0 o l O 6 7 E 04 0 o l l 3 9 E 04 0 0 1 2 3 1 E 04 0 o f 2 4 2 E 04 0 0 1 1 8 5 E 04 6 0 0 1 0 6 7 E 04 0 o 1 0 5 3 E 04 O o 1 1 2 6 E 04 0 0 1 2 1 9 E 04 0 o 1 2 3 1 E 04 G o 1 1 7 2 E C 4 7 0 . 1 0 5 3 E 04 0 .1039E 04 0.1113E 04 0.1208E 04 0.1219E 04 0 o 1 1 5 9 E 04 8 O o 1 0 3 9 E 04 0 o 1 0 2 5 E 0 4 Co11CCE 04 0 0 1 1 9 6 E 04 0 0 1 2 0 8 E 04 0 o 1 1 4 6 E 04 9 0 o 1 0 2 5 E 04 0 o 1 0 1 2 E 04 0.1087E 04 0 0 1 1 8 5 E 04 0 o 1 1 9 6 E 04 0 o 1 1 3 3 E 04

10 O e 1 0 1 2 E 04 G.9979E C 3 0 .1074E 04 0 0 1 1 7 3 E 04 0.1185E 04 0 o 1 1 1 9 E 04 11 0 0 9 5 7 9 E 03 0 o 9 8 4 2 E 03 0 0 1 0 6 1 E 04 O e 1 1 6 2 E C 4 O o 1 1 7 3 E 04 0 0 1 1 0 6 E 06 12 O o Y 8 4 2 E C3 0 o 9 7 0 5 E 03 0 o 1 0 4 8 E 04 0 0 1 1 5 0 E 04 0 o 1 1 6 2 E 04 0 o 1 0 9 3 E 04 13 0 . 9 7 0 5 E 0 3 0 .9569E 03 C o l G 3 5 E 04 0.1139E 04 0.115GE 04 0 . 1 0 8 0 E 04 14 0 o 9 5 6 9 E 03 0 0 9 4 3 3 E 03 0.1C22E 04 0 0 1 1 2 8 E 04 0 0 1 1 3 9 E 04 0 o 1 0 6 7 E 04 15 0 0 9 4 3 3 E 05 0 o 9 2 9 7 E 03 0 0 1 0 0 9 E C 4 0 0 1 1 1 6 E 04 0 0 1 1 2 8 E 04 0 0 1 0 5 3 E 04 16 0 o 9 2 9 7 E 03 0 . 9 1 6 2 E 03 ( 3 0 9 S 5 7 E 03 0 0 1 1 0 5 E 04 O o l l l O E 04 0 . 1 0 4 0 E 04 17 0 0 9 1 6 2 E 0 3 0 0 9 0 2 9 E G 3 0 0 9 8 2 7 E 03 O e 1 0 9 4 E 04 0 o 1 1 0 5 E 04 0 o 1 0 2 7 E 04 1 8 0 0 9 0 2 9 E 03 0 0 8 8 9 5 E G3 C 0 9 t 9 7 E 03 0 0 1 0 8 3 E 04 0 0 1 0 9 4 E 04 0 o 1 0 1 4 E 04 19 C o 8 8 9 5 E 0 3 C.8763E C 3 0 . 9 5 6 8 E C3 0 . 1 0 7 2 E 04 0 o l G 8 3 E 04 O . l G 0 0 E 04 20 0 0 8 7 6 3 E 0 3 0 0 8 6 3 2 E 03 ( 7 0 9 4 3 S E 03 0.1061E 04 0 0 1 0 7 2 E 04 0 0 9 8 7 1 E 03 2 1 0 0 8 6 3 i E 03 0 o 8 5 0 3 E 0 3 00931 l .E C 3 0 o 1 0 5 0 E 04 0 0 1 0 6 1 E 04 0 o 9 7 3 9 E 03

TWDT

F

0 0 1 5 4 9 E C 2 C a 4 5 2 8 E 02 o3 0 o 4 5 1 6 E 02 .I O o ' i 5 2 5 E 02 0 0 4 5 3 3 E 02 C o 4 5 3 8 E 02 0 0 4 5 4 0 E 02 0 0 4 5 4 0 E G 2 0 o 4 5 3 8 E 0 2 0 0 4 5 3 2 E 02 0 0 4 5 2 4 E 0 2 0 0 4 5 1 3 E C 2 0 o 4 4 9 9 E @2 0 0 4 4 8 2 E 0 2 0 0 4 4 6 2 E C2 Oo444CIE 02 0 0 4 4 1 4 E C2 0 0 4 ' 3 8 5 E 0 2 0 . 4 3 5 3 E 02 0 0 4 3 1 8 E 02 0 0 4 2 8 C E 0 2

I

1 2 3 4 5 6 7

9 1 G 11 1 2 1 3 14 1 5 1 6 17 1 8 1 9 20 2 1

a

VI1

0.0 6 .1833 60 1 6 4 9 6 . 1 4 6 7 6.1286 6. I 1 0 6 6.0926 6 , 0 7 4 8 60057G 6 0 0 3 9 4 6.0219 6 0 0 4 5 5.9672 5.9702 5.9532 5 ,9365 5.9199 5 , 9 0 3 5 50 8873 5.8713 5.8555

v 2 v 3

F T / S E C

O m 0 6.9424 6.S 21 8 6.9C14 6.8810 6 . 8 t 0 8 6.8406 6. 8 206 6 , 8 0 0 6 6.78C 8 6.761 2 6.741 6 6.7 2 2 3 6. 7 0 3 1 6.6841 6.6653 6. 6 4 6 7

6.6101 6.5921 6. 5 744

6.6 283

G o 0 6.7222 6 .7022 6 0 6825 6.6628 6.6432 6 0 6 2 3 6 6 0 6042 6 .584s 60 5658 6a 5467 6.5278 60 5C91 6 ,4905 6 .4721 6 , 4 5 3 9 6 ,4358 6.4180 6 , 4 0 0 4 60 3830 6.3659

v W l

0.0 6.3719 6,3530 6.3342 6.3155 6.2970

6.2601

6. 2 236 6. 2055 6.1876 6.1699 6.1522 6.1348 6,1175 6. 1 0 0 4 6,0836 6.0669 6.0504 6.0341

6.2785

6.2418

v w3

0.0 7.6251 7.6025

7.5577 7 .5355 7.5133 7 .4913 7 .4694 7 04477 7.4261 7 .4046 7.3834 7 0 3 6 2 3 7 . 3 4 1 4 7.3208 7.3003 7 .2801 7 ,2601 7. 2 4 0 4 7.2210

7.5801

PDSO PDTO

LB/SQFT

847.431 2 847.4312 841.4097 835.4158

a 17.443

8 2 9 , 4.214 823.4249

8 1 1.4666 805o5016 7990 5500 793.6187 7 8 7 o 7 1 0 0

775.9714 770.1499 704.365 2 758 ,6204 75 2.9199 747.2676 741.6660 736.1208

781 . a 259

2869,1321 861.8818 853.9431 846.0403 a38.1379 8 a30.2402 2 2.3506

814.4746 806.6165 798.7803 7 9 0 , 971 2 783.1538

co co

i 75.4529 967.75 29 760.0996 75 2.4968 '144.9495 737 .4034 730oG410 722.6892 7 1 5 . 41 14

I

1 2 a 4 5 6 7 8 9

10 11 12 13 14 15

4

16 17 18 i s 20 2 1

RENT0

0.1138E 05 0.1091E 05 0.1061E 0 5 0.1031E 05 0.100lE 05 009721E 04 0.9434E 04 0.9151E 04 008874E 0 4 008601E 04 008333E 0 4 OoBO71E 0 4 0.7814E 04 0.7562E 0 4 007316E 0 4 007075E 04 0.6840E 04 0.6611E 04 0.6389E 04 0.6172E 04 3.5961E 04

PRNTC

0.8232E 0 1 0.8589E 0 1 008835E 0 1 0.9092E 0 1 0.9360E 0 1 0.9641E 0 1 009934E 0 1 001024E 0 2 001056E 0 2 0.1090E 0 2 0.1125E 0 2 001161E 0 2 001199E 0 2 0.1239E 0 2 001281E 0 2 0.1325E 02 0.1370E 0 2 001417E 02 0.1467E 0 2 001518E 0 2 001572E 02

R E N S O l

0.0 0m2887E 05 C.2822E 05 0.2758E 05 0:2695E 05 0.2631E 05 0.2568E 05 002506E 05 0o2443E 05 0.2382E 05 0.232CE 05 Co226CE 05 002199E 05 002140E 05 002081E 05 002023E 05 0.1966E 05 0.191CE 05 0.1854E 05 C.18CCE 05 00174tE 05

RENSOZ

0.0 0m3241E 05 0.3169E 05 0.3097E 05 0.3026E 05 002955E 05 002884E 05 0m2813E 05 0.2743E 05 002674E 05 0.2605E 05 002537E 05 002469E 05 0m2403E 05 002337E 05 0.2272E 05 0.2207E 05 0.2144E 05 0.2082E 05 0.2021E 05 001961E 05

REkS03

0.0 0.3138E 05 003068E 05 0.2999E OS 002930E 05 002861E 05 002792E 05 0m2724E 05 002656E 05 0.2589E 0 5 0.2523E 05 0.2456E 05 0.2391E 05 002326E 05 0.2263E 05 0.2199E 05 0.2137E 05 0.207tc 05 0.2016E 05 0.1956E 05 0.1898E 05

HTO AHSO UOA

BTU/ HR / S QF T / F

0.17326 04 0.3422E 04 0.3318E 04 0.3232E 04 0m3147E 04 Oo3063E 04 0.2979E 04 0.2896E 04 0.2814E 04 0.2732E 04 0m2651E 04 0.2571E 04 0.2492E 04 0m2413E 04 0.2335E 04 002258E 04 0m2183E 04 002108E 04 002034E 04 0m1961E 04 001889E 04

005314E 03 0.2580E 04 002532E 04 002507E 04 0.2481E 04 0.2456E 04 0.2430E 04 0m2403E 04 0.2377E 04 0.2351E 04 0m2324E 04 0.2298E 04 0m2271E 04 0m2245E 04 002218E 04 0.2192E 04 0m2165E 04 002139E 04 0.2112E 04 0m2086E 04 0.2059E 04

003653E 03 0m1044E 04 0.1026E 0 4 0.1014E 04 0ml001E 0 4 009881E C 3 009751E 03 0m9619E 03 0o9485E 03 0.9349E C ? 0.9211E C 3 0.9071E 03 0.8929E 03 0.8786E 03 008640E C ? 0.8493E 03 0m8345E 03 0.8194E 0 3 0.804ZE C 3 0m7888E 0 3 007733E 03

HE AT

BTU/HR

0.1793E 09 008700E C e 0.8678E C 8 0.8695E 08 Co8710E 08 C.871SE C8 0.872*E 08 0.8724E C 8 0.8719E 08 0.87CBE C 8 Cm86oZE 08 008672E C 8 0.8645E C 8 C.8612E 08 0.8574E 08 0.8531E C8 \o

0m8481E 08 008426E 08 Ca8364E C8 0m8297E 08 008224E 08

117

P (SOPT) AN0 THE ALLOWABLE TUBE S I D E DELTA-P (DELPTA)

YES NO

I CHECK TO SEE I F SOP1 I S WITHIN 3% OF DELPTA 1 ADJUST THE NUMBER OF TUBES I N THE EXCHANGER (NUNT) A I

1 I CALCULATE THE DIFFERENCE BETWEEN THE TOTAL SHELL S l O E DELTA-

P (SOPS) AND THE ALLOWABLE SHELL S I D E DELTA-P (DELPSA)

CHECK TO SEE I F SOPS I S WITHIN 3% OF DELPSA

ADJUST THE BAFFLE SPACING (BS(K))

i ALL OF THE HEAT HAS BEEN TRANSFERRED--THE TOTAL PRESSURE OROPS ON BOTH TUBE AN0 SHELL SIDE ARE W I T H I N L I M I T S . WE HAVE AN ACCEPTABLE SOLUTION. \ WRITE OUT THE RESULTS.

Fig . D. 1. (cont inued)

M S = l S X = O SBS=O T C ( l ) = T C 2 T H ( l ) = T H 1 R WK =DT O*LC.G F ( C TO/D T I 1 / Z O O P C ( 1) =PC2 CALL S V H ( P p P C f t T C Z t C U C t H C ( 1 I 1 B N = F L O A T f ( N J QX=QT/ BN O E C T = Q X / ( hH*CPt-) DEC H= QX/ WC 1=1 K= 1

L O P 7 = 0 16 SB = SBK*BSL

TCON=TH( I J-DTPE/2oC I F ( I o E O o 1 ) GO TO 162 V M U O = O o 2 1 2 2 * E X P F ( 4 0 3 2 o / ( T W + 4 6 0 . ) ) V M U B ~ O o 2 1 2 2 * E X P F ( 4 0 3 2 o / ( T C O N + 4 6 O o 1 1 FACT=( VH UC/ VH Ir 6 1 **0.14 GO TO 1 6 2

161 F A C T = l o O 162 CONTINUE

DE"= 1 41 38 E + C C-2.4 t 6 E - 0 2* TC ON V I SH=O 0 2 1 2 2 € + 0 0 * E X P F ( 403 2oGE+bO / ( TCON+460o 0 E+GO 1 1 DHOT( K )=DE" VHOT( K 1=V 1SP

GM=WH/ Si3 RECB=DTO* EM/V ISH

C O N l = ( CPH *V IS )./TCH 1 * * G o 6 C 7 E +OU

IF( RECB-800.0 l l 7 t 1 8 t l e 17 HJB=Om 5 7 1 /( RECB**Oo456)

G O T 0 1 9

19 HB= (HJ B*C PH*GC/CON 1 1 *FACT GW =WH/ SW GS=SQRTf ( G M * G b I l RECW=DTO* CS /V I S H

18 HJt i=Oo 346/( RECB**Oo 382)

IF4 R E C W - 8 0 G . O 1 2 0 p 2 1 9 2 1

SUP 1030 SUP 1030 SUP 1c4c SUP 1050 SUP 1060 SUP IO73 SUP l C P 0 SUP 1 0 9 C SUP 1100 SUP l l l C SUP 1 1 2 0 SUP 1130 SUP 1140 SUP 1150 SUP 1 1 6 Q SUP 1170 SUP 1 1 8 0 SUP*11 e 1 SUP* l l a ? SUP*1183 SUP* 11 94

SUP*1186 SUP*? 1 8 1 SUP 1190 SUP ? 2 C G SUP l 2 l G SUP 132G SUP 1 2 3 C SUP 124C SUP 1 2 5 C SUP 126@ SUP 1 2 7 0 SUP 1 2 8 0 SUP 1290 SUP * 1300 SUP 1310 SUP 1 3 2 0 SUP 1330 SUP 1340

s u ~ i i a 5

2 0 H J Y = O o 571 / ( RECW**Oo456)

2 1 HJW=O. 346/( RECW**0.382 J GO TO2 2

2 2 HW=(HJW*CPH*GS/CONl )*FACT

SUP 1350 SUP 136U SUP 137G SUP* 13 80

23

24

25

26

M

28

29

30 31

32

33

HO=(HB*( 1 oO02oC*PW J+HY*( 2.0*PWJ )*BLFH SUP 1390 HO = w w e w SUP 1 4 0 C

SUP 1410 TH( I + 1 )=Tk ( 1)-DECT SUP 1420 LOP5=O SUP 143@ HC( I + l )=HC( 1)-CECH SUP 1440 OELPP=O.O SUP 1450 PC ( I + l )=PC( I ) +CELPP SUP 146@ LOP3=0 SUP 1470 LOP4=O SUP 1490 T C I 1+1 )=TC( I)=D€CH SUP 149c CALL S V H ( 29PC (I+1! r l C ( I + l ) rDUH9tKGJ SUP 1500

SUP 1510 EH=ABS F ( HC( I + 1 1-HC G 1 I F ( EH-00 OC1*).C( 1+1 J J 3 1 9 3 1 9 2 6 SUP 1 5 2 0 TRIAL=TC( 1+1J SUP 153C HR IAL=HCG SUP 154c TC ( I + 1 1 =TC ( I+ 1 1 +( HC ( I +1 I-HCG 1 * ( TC ( I 1- TC f I + I ) 1 / i HC ( I 1 -HCG 1 SUP 155C CALLSVHt 2 9PC( I+l)rTC( I+1) rOUH9HCG1 SUP 1560

SUP 1570 EH=ABSF(HC( I + 1 J-HCG) IF ( EH-O.OC1 *HC ( I+1) 1 3 1 9 3 1 9 2 8 SUP 1 5 8 C TNEXTt TC 4 I + 1 J + (HC I I + 1 I-HCG 1 * ( TC ( I +1 J-TR I P L J /(HCG-HR I A L J SUP 1 5 9 C TRIAL=TC( I + l ) SUP 1600 HRIALrHCG SUP 1610 TC( 1+1 I=TNEXT SUP 1 6 2 C LOP3=LOP3+1 SUP 1630 IF (LOP3-1CJ30 r30r29 SUP 1640 WR I TEOUTP UTTA PES19 1 0 1 5 9 LOP3 SUP 1650 GOT080 SUP 1660 GOT027 SUP 1670 DENOMs(TH(I+11-TC( I + l ) ) / ( T H ( I J - T C ( I 4 ) SUP 1680 TOEWABSF ( D E N C N - l o O ) SUP 169L I F (TDEN-0.051 32933933 SUP 1700 DELTLM=OoSE+OC*(TH( I + l ) - f C ( I + l J + T H ( I I - T C ( I I J SUP 1710 GO TO 34 SUP 172@ DELTLM=(Tb( I + ] ) - T C ~ I + 1 ~ ~ ~ H ~ I ~ + T C ( I ) ~ / L O G F ~ ~ T H ~ I + l J - T C ~ I + l ~ J / ~ T H ~ l JSUP 1 7 3 C

l - T C ( I J ) ) SUP 1731

RO( K ) = l o 0 /HC

ORNL TM- 2815

Contract No. W-7405-eng-26

Genera 1 Engineering Divi s ion


C. E . Bet t is T. W. P icke l W. K. Crowley M. Siman-Tov H. A . Nelms W. C. Stoddart

APRIL 1971 L E G A L N O T I C E

This report was prepared as sponsored by the United States the United States nor the United States Atomic Energy Commission, nor any of their employees, nor any of their contractors, subcontractors, or their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights.

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee

operated by U N I O N CARBIDE CORPORATION

f o r the U.S . ATOMIC ENERGY COMMISSION

D w m T i O N OF TEilS DOCUMENT IS UNLI-

v .

iii

CONTENTS

.

A b s t r a c t ......................................................... 1

1 . INTRODUCTION ................................................. 1

2 . PRIMEX. THE PRIMARY HEAT EXCHANGER PROGRAM ................... 3

2 .1 D e s c r i p t i o n of P r i m a r y H e a t E x c h a n g e r ................... 4

2.2 Design C a l c u l a t i o n s ..................................... 8

2.3 Descript ion of PRIMEX ................................... 1 6

2 . 4 E v a l u a t i o n of PRIMEX .................................... 17

3 . RETEX. THE STEAM REHEATER EXCHANGER PROGRAM .................. 19

3 . 1 D e s c r i p t i o n of S t e a m R e h e a t e r ........................... 20

3 . 2 D e s i g n C a l c u l a t i o n s ..................................... 23

3 . 3 Descr ip t ion of RETEX .................................... 23

3 . 4 E v a l u a t i o n of RETEX ..................................... 24

4 . SUPEX. THE STEAM GENERATOR SUPERHEATER PROGRAM ............... 26

4.1 D e s c r i p t i o n of S t e a m Generator .......................... 27

4 . 2 Design C a l c u l a t i o n s ..................................... 29

4 . 3 Descript ion of SUPEX .................................... 37

4.4 E v a l u a t i o n of SUPEX ..................................... 39

REFERENCES ....................................................... 41

A p p e n d i x A: PHYSICAL PROPERTY DATA .............................. 45

A p p e n d i x B : THE PRIMEX P R O G h .................................. 4 9

Appendix C : THE RETEX PROGRAM ................................... 90

A p p e n d i x D: THE SUPEX PROGRAM ................................... 114

v

Figure Number

2.1

2.2

3.1

4 .1 B . l

c. 1

D. 1

V

LIST OF FIGURES

T i t l e Page

Number

Cross-Sect ional Eleva t ion of a Typical MSBR Primary 5 H e a t Exchanger

Zones of Flow Between Two Baf f l e s i n the S h e l l Side 1 2 of the MSBR Primary Heat Exchanger

Typical MSBR Steam Reheater Exchanger 2 1

27

50

91

115

Typical MSBR Steam Generator Superheater Exchanger

S impl i f ied Flow Diagram of the PRIMEX Computer Program

Simpl i f ied Flow Diagram of the RETEX Computer Program

Simpl i f ied Flow Diagram of the SUPEX Computer Program

.

Tab le Numb e r

2 . 1

3.1

4.1

4.2

4.3

A. 1

A . 2

A. 3

B. 1

B . 2

c. 1

c. 2

D. 1

D. 2

v i i

LIST OF TABLES

T i t l e

Design Data f o r MSBR Primary Heat Exchanger

Design Data f o r MSBR Steam Reheater Exchanger

Design Data f o r MSBR Steam Generator Superheater Exchanger

Pre l iminary S t r e s s Ca lcu la t ions f o r MSBR Steam Genera t o r

Percentage Deviations Resul t ing From Ca lcu la t iona l U n c e r t a i n t i e s Related t o MSBR Steam Generator Exchanger

Design P r o p e r t i e s of MSBR Fuel S a l t

Design P r o p e r t i e s of MSBR Coolant S a l t

Design P rope r t i e s of Has te l loy N

Computer Input Data f o r PRIMEX Program

Output Data From PRIMEX Program

Computer Input Data f o r RETEX Program

Output Data From RETEX Program

Computer Input Data f o r SUPEX Program

Output Data From SUPEX Program

Page Number

6

20

28

37

40

46

47

48

53

54

94

95

118

119

1


Ab s t r a c t

Three computer programs were developed t o make design c a l c u l a t i o n s f o r the h e a t exchangers f o r Molten-Salt Breeder Reactor concepts. They a r e the program f o r the primary h e a t exchangers, PRIMEX; the program f o r the r e h e a t e r s , RETEX; and the program f o r the steam gene ra to r supe rhea te r s , SUPEX. Each type of exchanger analyzed i s desc r ibed , the b a s i c equa- t i o n s used i n each a n a l y s i s a r e given, and the l o g i c used i n each program i s discussed b r i e f l y i n t h i s r e p o r t . Flow d i a - grams, l i s t s of i npu t r equ i r ed and output r ece ived , complete program l i s t i n g s , and the nomenclature f o r the programs a s w e l l a s example computer i npu t and ou tpu t f o r the exchangers desc r ibed a r e appended.

1. INTRODUCTION

The concept of a s i n g l e - f l u i d Molten-Salt Breeder Reactor (MSBR)

wi th a thermal c a p a c i t y of 2250 MW and a n e t e l e c t r i c a l ou tpu t of 1000 MW

has some very s p e c i a l h e a t exchange requirements. I n the p r e s e n t concep-

t u a l design f o r the MSBR p l a n t , t h e r e a r e f o u r h e a t exchangers i n the

primary system t h a t t r a n s f e r h e a t from the molten f l u o r i d e f u e l - s a l t mix-

t u r e t o the m o l t e n s o d i u m f luorobora te coo lan t s a l t . In the secondary

system, t h e r e a r e e i g h t r e h e a t e r s and 16 steam gene ra to r s t h a t t r a n s f e r

h e a t from the coolant s a l t . The manner i n which these exchangers were

designed t o m e e t t he s p e c i a l h e a t exchange requirements and the computer

programs t h a t were developed t o c a l c u l a t e the design numbers a r e descr ibed

i n t h i s r e p o r t . The development of MSBR concepts passed through a number of s t a g e s

during which the p l a n t layout was improved, core conf igu ra t ions were

optimized, and phys ica l p rope r ty d a t a were r e f i n e d . The f i r s t formal

s tudy of a MSBR h e a t exchange system made by the au tho r s was r epor t ed i n

1967 (GE&C Divis ion Design Analysis Sec t ion , "Design Study of a Heat-

Exchange System For One MSBR Concept," USAEC Report ORNL TM-1545, Oak

2

Ridge Nat ional Laboratory, September 1967). To analyze one exchanger a t

each s t a g e of i t s subsequent development without programming a l a rge por-

t i o n of the necessary c a l c u l a t i o n s would have meant almost con t inua l r e p -

e t i t i o n of these c a l c u l a t i o n s over a per iod of many months.

p u t e r programs a v a i l a b l e , the design f o r an exchanger could e a s i l y be

updated f o r changed c a p a c i t y , phys i ca l p r o p e r t i e s , temperatures , p re s -

s u r e s , e t c .

With com-

Three such computer programs were developed. One computer program

was w r i t t e n t o make the design c a l c u l a t i o n s f o r the primary h e a t

exchanger, and i t i s the PRIMEX program. This program was modified a t

one s t a g e of i t s development t o perform the c a l c u l a t i o n s f o r the steam

r e h e a t e r exchangers. This modified ve r s ion i s the RETEX program. A

t h i r d computer program was w r i t t e n t o perform the design c a l c u l a t i o n s f o r

the steam gene ra to r supe rhea te r exchangers, and i t i s the SUPEX program.

The design d a t a f o r each of these t h r e e types of exchanger, the b a s i c

equat ions used i n each design a n a l y s i s , and each of the computer programs

developed t o perform the a n a l y s i s a r e descr ibed i n the fol lowing s e c t i o n s

of t h i s r e p o r t . Flow c h a r t s f o r each program, l i s t s of the inpu t

r equ i r ed and the output provided by each program, complete program l i s t -

i n g s , nomenclature l i s t s f o r each program, and the computer i n p u t and

output f o r each type of h e a t exchanger discussed a r e appended.

V

3

2 . PRIMEX, THE PRIMARY HEAT EXCHANGER PROGRAM

There a r e f o u r primary h e a t exchangers, which t r a n s f e r h e a t from the

f u e l s a l t t o the coolant s a l t , i n the conceptual design f o r a s i n g l e -

f l u i d MSBR. Each of t hese exchangers has a thermal capac i ty of 556 MW

and each i s of the same design. The f u e l s a l t c i r c u i t s f o r the primary

h e a t exchangers a r e i n p a r a l l e l , each having i t s own f u e l pump. The

coo lan t s a l t from each exchanger i s c i r c u l a t e d through i t s own system of

two r e h e a t e r exchangers and fou r steam gene ra to r s .

A t f u l l design load, t he f u e l s a l t e n t e r s the top of t he primary

h e a t exchanger a t a temperature of 1300°F and e x i t s from the bottom a t a

temperature of 1050°F f o r r e t u r n t o the r e a c t o r . The coo lan t s a l t a t a

temperature of 850°F e n t e r s the top of the primary h e a t exchanger and i s

d i r e c t e d t o the bottom of the exchanger through a c e n t r a l downcomer where

i t e n t e r s the s h e l l s i d e of the exchanger, flows upward i n counterflow

t o the f u e l s a l t , and leaves the top of t he exchanger a t a temperature of

1150°F. This coo lan t s a l t i s c i r c u l a t e d through the steam r e h e a t e r s and

steam gene ra to r s where i t s h e a t i s t r a n s f e r r e d t o the exhaust steam and

feedwater , r e s p e c t i v e l y . The design cond i t ions f o r the primary h e a t exchanger were p a r t i a l l y

The h e a t load, d i c t a t e d by the o v e r a l l requirements of the MSBR system.

en t r ance and e x i t temperatures of t h e f u e l and coolant s a l t s , and the

maximum o r des i r ed p res su re drops a c r o s s the s h e l l and tube s i d e s of the

exchanger were s p e c i f i e d by the o p e r a t i n g cond i t ions of the system.

Design cons ide ra t ions f o r t he o v e r a l l system d i c t a t e d the type of

exchanger, arrangement of nozzles t o f a c i l i t a t e p i p i n g , minimum tube

diameter considered t o be c o n s i s t e n t w i th f a b r i c a t i o n p r a c t i c e s , and the

l i m i t on the o v e r a l l l eng th of the exchanger. C e r t a i n c r i t e r i a such a s

the maximum al lowable temperature drop a c r o s s the tube w a l l s and the need

t o b u i l d i n enough tube f l e x i b i l i t y t o compensate f o r d i f f e r e n t i a l t he r -

mal expansion were e s t a b l i s h e d by the s t r e n g t h of t he m a t e r i a l s . Vibra-

t i o n cons ide ra t ions placed l i m i t s on flow v e l o c i t i e s and the spacing

between b a f f l e s . I n a d d i t i o n , i t i s h i g h l y d e s i r a b l e t h a t the volume of

f u e l s a l t be kep t a t a minimum t o lower the doubling time of the r e a c t o r .

Within the framework of these requirements and g u i d e l i n e s , a

computer program was developed t o perform a parameter s tudy and s e l e c t

t he design f o r the primary h e a t exchanger t h a t employs a minimum volume

of f u e l s a l t . The design d a t a and equat ions discussed i n the fol lowing

subsec t ions were used t o develop the computer program f o r the primary

h e a t exchanger (PRIMEX).

2 . 1 Descr ipt ion of Primary Heat Exchanger

Each of the fou r primary h e a t exchangers i s a v e r t i c a l she l l - and-

tube type with a s i n g l e counterflow pass on both the tube and s h e l l s i d e s .

Each u n i t i s about 6 f t i n diameter and about 22 f t t a l l , no t i nc lud ing

the coolant s a l t U-bend p i p i n g a t t he top. A c r o s s - s e c t i o n a l e l e v a t i o n

of a t y p i c a l primary h e a t exchanger i s i l l u s t r a t e d i n Fig. 2 . 1 , and the

p e r t i n e n t design d a t a a r e given i n Table 2.1.

The f u e l (primary) s a l t e n t e r s the tube s i d e of the primary h e a t

exchanger a t the top and flows ou t the bottom of the exchanger a f t e r a

s i n g l e pass through the 3/8-in.-OD tubes. The coo lan t (secondary) s a l t

e n t e r s a t the top of the exchanger, flows t o the bottom o f the exchanger

through a c e n t r a l 20-in.-diameter downcomer where i t e n t e r s the annular

s h e l l con ta in ing the tubes, flows upward around modified d i s k and dough-

nut b a f f l e s , and e x i t s through a 28-in.-diameter p i p e concen t r i c w i th the

i n l e t pipe a t the top.

The tubes a r e arranged i n concen t r i c r i n g s i n the bundle wi th a con-

s t a n t r a d i a l p i t c h and a c i r c u m f e r e n t i a l p i t c h t h a t i s a s cons t an t a s

can be obtained. The L-shaped tubes a r e welded i n t o a h o r i z o n t a l tube

s h e e t a t the bottom and i n t o a v e r t i c a l tube s h e e t a t the top. The

toroidal-shaped top head and tube s h e e t assembly has a s i g n i f i c a n t

s t r e n g t h advantage, s i m p l i f i e s the arrangement f o r c o o l a n t - s a l t f low, and

allows the s e a l weld f o r the top c losu re t o be loca ted o u t s i d e the h e a t

exchanger.

To accommodate d i f f e r e n t i a l thermal expansion between the s h e l l and

tubes, about 4 f t of the upper p o r t i o n of the tubing i s ben t i n t o a s i n e

5

PRIMARY SALT

/ \

ORNL-DWG 69-6004

Fig. 2 . 1 . Cross-Sect ional Eleva t ion of a Typical MSBR Primary He a t Exchanger.

6

Table 2.1. Design Data f o r MSBR Primary Heat Exchanger

Number r equ i r ed

Rate of h e a t t r a n s f e r p e r u n i t , Mw Btu/hr

Tube-side cond i t ions Hot f l u i d Entrance temperature, OF E x i t temperature , O F

Entrance p r e s s u r e , p s i Pressure drop ac ross exchanger, p s i Mass flow r a t e , l b / h r

Cold f l u i d Entrance temperature, O F

E x i t temperature, "F E x i t p r e s s u r e , p s i Pressure drop ac ross exchanger, p s i Mass flow r a t e , l b / h r

Materia 1 Number r equ i r ed P i t c h , i n . Outside diameter , i n . Wall t h i ckness , i n . Length, f t

Tube shee t Materia 1 Thickness, i n . Sheet- to-sheet d i s t a n c e , f t

To ta l h e a t t r a n s f e r a r e a , f t 2 Basis f o r a r e a c a l c u l a t i o n

Volume of f u e l s a l t i n t ubes , f t 3

She 11

S h e l l - s i d e cond i t ions

Tube

Mater ia 1 Thickness, i n . I n s i d e diameter , i n .

Cen t r a l tube diameter , i n .

Ba f f l e Type Numbe 1: Spacing, i n .

Shell-and-tube one-pass v e r t i c a l exchanger with d i s k and dough- nu t b a f f l e s

Four

556.5 1.9 x 10"

Fuel s a l t 1300 1050 180 130 23.45 X lo6

Coolant s a l t 850 1150 34 116.2 17 .8 x lo6

Has te l loy N 5896 0.75 0.375 0.035 22.57

Has te l loy N 4.75 21.31

13,037 Outside of tubes

67.38

Has te l loy N 0.5 68.07

20.0

Disk and doughnut 2 1 11.23

W

Y

7

Table 2 . 1 (cont inued) ~ _ ~ _

Disk o u t s i d e diameter , i n . 54.56

Doughnut i n s i d e diameter , i n . 45.54

Overa l l h e a t t r a n s f e r c o e f f i c i e n t , U ,

Tube

Btu/hr f t2 O F 838.3

Maximum primary (P) stresses Ca lcu la t ed , p s i 674 Allowable, p s i 3912

Maximum primary and secondary (P + Q) stresses Ca lcu la t ed , p s i 11,639 Allowable, p s i 11,737

Ca lcu la t ed , p s i 13,006 Allowable , p s i 25 , 000

Maximum peak (P + Q + F) s t r e s s e s

wave conf igu ra t ion . The tubes a r e he ld i n p l ace by w i r e l a c i n g i n t h i s

upper p o r t i o n of the tube bundle. Since b a f f l i n g i s no t employed i n

t h i s r eg ion , t he bent- tube p o r t i o n of the bundle experiences e s s e n t i a l l y

p a r a l l e l flow and a r e l a t i v e l y lower h e a t t r a n s f e r performance.

Below the bent- tube region of the bundle, evenly spaced doughnut-

shaped b a f f l e s a r e used t o hold the tubes i n p l ace and t o produce c r o s s

flow. The b a f f l e spacings and cross-f low v e l o c i t i e s a r e designed t o min-

imize the p o s s i b i l i t y of flow-induced v i b r a t i o n . The tubes i n t h i s ba f -

f l e d region of the h e a t exchanger have a h e l i c a l i n d e n t a t i o n knurled

i n t o t h e i r s u r f a c e t o enhance the f i l m h e a t t r a n s f e r c o e f f i c i e n t s and

thereby reduce the f u e l s a l t inventory i n the exchanger. N o enhancement

of t h i s n a t u r e was used i n the upper ben t - tube region because of p r e s e n t

u n c e r t a i n t y about the r e l i a b i l i t y of tubes t h a t a r e both ben t and

indented.

8

2 . 2 Design Ca lcu la t ions W

Since experience with both the f u e l and coo lan t s a l t s i s l i m i t e d ,

t he re was and s t i l l i s a c e r t a i n degree of u n c e r t a i n t y a s s o c i a t e d with

the t r a n s p o r t p r o p e r t i e s of s a l t and i t s behavior a s a h e a t t r a n s f e r

medium. The design p r o p e r t i e s of t he f u e l s a l t , coolant s a l t , and of

Has te l loy N used i n the concept of a s i n g l e - f l u i d MSBR and incorporated

i n the primary h e a t exchanger computer program a r e given i n Appendix A.

A s prev ious ly desc r ibed , the tubes i n the b a f f l e d p o r t i o n of the

primary h e a t exchanger a r e h e l i c a l l y indented t o improve h e a t t r a n s f e r

performance. Experiments performed by C. G. Lawson, R. J. Kedl, and R.

E . McDonald i n d i c a t e d t h a t t h i s i nden ta t ion i s expected t o r e s u l t i n an

improvement by a f a c t o r of 2 i n the tube-side h e a t t r a n s f e r c o e f f i c i e n t .

An enhancement f a c t o r of 1 . 3 fo r the h e a t t r a n s f e r c o e f f i c i e n t ou t s ide

the tubes i s suggested by Lawson2 although no experiments have been done

t o support t h i s recommendation. The experimental work t h a t was per-

formed w a s l i m i t e d t o Reynolds numbers g r e a t e r than 10,000, and t h e r e i s

some u n c e r t a i n t y about the degree of improvement t h a t can be expected f o r

Reynolds numbers of l e s s than 10,000. I t was assumed t h a t no improvement

can be expected i n a t r u l y laminar flow (Reynolds numbers l e s s than l O O O ) ,

and the improvement expected f o r the in t e rmed ia t e range was e x t r a p o l a t e d

by us ing a method suggested by H. A . M ~ L a i n . ~ The r e s u l t i n g enhancement

f a c t o r s (EF) a r e

1

1

EFi = 2.0 and EFo = 1.3 f o r Reynolds numbers 2 10,000

and

EFi = 1.0 and EF = 1.0 f o r Reynolds numbers - < 1000, 0

where

EFi = enhancement f a c t o r i n s i d e tube and

EFo = enhancement f a c t o r ou t s ide tube ( c ros s f low).

For 1000 < Reynolds number < 10,000,

1 I2 EFi = 1.0 i- [ N k 9 ~ o ~ o o o ]

and

9

- 1000 JJ2 EF = 1.0 + 0.3( NRe 9ooo )

0

where N = the corresponding Reynolds number. Re The enhancement f a c t o r s f o r h e a t t r a n s f e r r e s u l t i n g from the h e l i c a l

i n d e n t a t i o n of the tubes i n the b a f f l e d region were assumed t o have a

p ropor t iona te e f f e c t on p res su re drop. The s h e l l - s i d e p re s su re drop was

c a l c u l a t e d by us ing the procedure r epor t ed by 0. P. Bergel in e t a1. ,4 and

the tube-side p re s su re drop was c a l c u l a t e d by us ing the conventional

f r i c t i o n - f a c t o r method. An o v e r a l l leakage f a c t o r of 0.5 was used f o r

the p re s su re drop i n the s h e l l s i d e o f the h e a t exchanger, and a f a c t o r

of 0.8 was used i n the h e a t t r a n s f e r c a l c u l a t i o n s . These leakage f a c t o r s

were s e l e c t e d on the b a s i s of recommendations r epor t ed by Berge l in e t a l .

The c o r r e c t leakage f a c t o r , which i s dependent upon va r ious c l ea rances

between tubes and b a f f l e s and between b a f f l e s and the s h e l l , w i l l have

t o be c a l c u l a t e d when the a c t u a l design f o r the primary h e a t exchanger

has been completed .

5

Since molten f l u o r i d e s a l t s do no t w e t Has t e l loy N , the con ta in ing

m a t e r i a l of the h e a t exchanger, i t was suspected t h a t the usua l h e a t

t r a n s f e r c o r r e l a t i o n s , which a r e normally based on experiments with water

o r petroleum p roduc t s , might no t be v a l i d . However, r e c e n t experiments

performed by B . Cox i n d i c a t e d t h a t b a s i c a l l y the behavior of the f u e l

s a l t i s s i m i l a r t o t h a t of conventional f l u i d s . The c o r r e l a t i o n s devel-

oped by Cox r e s u l t i n h e a t t r a n s f e r c o e f f i c i e n t s somewhat lower than

those obtained from the S iede r and Tate c o r r e l a t i o n s f o r t u r b u l e n t

region^,^ Hansen's equa t ion f o r t r a n s i t i o n r eg ions ,

Tate c o r r e l a t i o n s f o r laminar region^.^ s tudy a r e those based on the d a t a developed by Cox t h a t w e r e recommended

by H. A. McLain. These a r e given i n E q s . 2.3, 2.4, and 2.5.

6

a and the S iede r and

The c o r r e l a t i o n s used i n t h i s

9

For completely t u r b u l e n t flow wi th Reynolds numbers g r e a t e r than

12,000,

where - - -

hi di - k. = 1

- - NRe NPr =

F b = P i - -

EFi =

10

h e a t t r a n s f e r c o e f f i c i e n t i n s i d e tube, Btu/hr . f t 2 * OF,

i n s i d e diameter of tube, f t ,

thermal conduc t iv i ty of f l u i d i n s i d e tube, B t u / h r . f t * O F ,

Reynolds number,

P rand t l number,

v i s c o s i t y a t temperature of bulk f l u i d , l b / h r - f t ,

v i s c o s i t y of f l u i d a t temperature of i n s i d e s u r f a c e of tube, l b / h r * f t , and

enhancement f a c t o r f o r h e l i c a l l y indented tubes given i n Eq. 2 . 1 .

Based on the i n s i d e diameter of the tube, the Reynolds number

diGi = -

NRe Pb

where Gi = mean mass v e l o c i t y of f l u i d i n s i d e the tube, l b / h r - f t 2 .

completely laminar flow wi th Reynolds numbers l e s s than 2100,

For

- hidi = ;1/ + ki

where = l eng th of tube from the en t r ance t o the l o c a l p o i n t , f t . For

the in t e rmed ia t e region where 2100 5 Reynolds number ,< 12000,

The p res su re drop i n s i d e the tubes was c a l c u l a t e d by u s i n g the

exp re s s ion

where

f = f r i c t i o n f a c t o r ,

L = l eng th of tube, f t ,

di = i n s i d e diameter of tube, f t ,

W

.

Y

11

v

. 2 = mean mass v e l o c i t y of f l u i d i n s i d e tube, l b l h r - f t ,

= d e n s i t y of f l u i d i n s i d e tube, l b / f t 3 , Gi

'i gc = dimensional conversion f a c t o r = 4.18 X lo8 Ib, .f t / lbf.hr*, and

EFi = enhancement f a c t o r f o r h e l i c a l l y indented tubes given i n E q . 2.1.

The f r i c t i o n f a c t o r f o r t u r b u l e n t flow (NRe > 2100) i s given by the

expres s ion f = 0.0014 i- 0.125(NR,) -0.32

>

and the f r i c t i o n f a c t o r f o r laminar flow ( N < 2100) i s given by the

exp re s s ion Re

16 f = - . NRe

The h e a t t r a n s f e r c o e f f i c i e n t across the tube w a l l i s given by the

expres s ion

where

k = thermal conduc t iv i ty , B tu /h r - f t*OF,

d = o u t s i d e diameter of tube, f t , 0

t = w a l l t h i ckness , f t , and

= i n s i d e diameter of tube, f t . di

No experiments have been performed t o d a t e t o develop c o r r e l a t i o n s

f o r the h e a t t r a n s f e r behavior of a sodium f luo robora t e coolant s a l t i n

the s h e l l s i d e of the h e a t exchanger. The c o r r e l a t i o n developed by 0. P.

Bergel in e t was used f o r the b a f f l e d region of the MSBR primary h e a t

exchanger, and the c o r r e l a t i o n developed by D. A. Donohuelo was used f o r

the unba f f l ed region.

Although s e l e c t e d a s being the most r e p r e s e n t a t i v e a v a i l a b l e f o r the

b a f f l e d r eg ion , Be rge l in ' s c o r r e l a t i o n * i s s t r i c t l y f o r c r o s s flow and

h i s d a t a were based on work wi th half-moon shaped b a f f l e s with s t r a i g h t

edges. Since d i s k and doughnut b a f f l e s a r e used i n the MSBR primary h e a t

exchanger, the adap ta t ion of Berge l in ' s d a t a involved c e r t a i n i n t e r p r e t a -

t i o n s i n determining the c r o s s - s e c t i o n a l a r eas involved. The c o r r e l a t i o n

1 2

f o r c ros s flow was a l s o modified by the i n t r o d u c t i o n of a c o r r e c t i o n

f a c t o r .

c ros s flow t h a t e x i s t s a s determined by the r a t i o between the b a f f l e

spacing and the annular t h i ckness of the v e s s e l . Data from Berge l in ' s

o r i g i n a l experiment4 were used t o e s t i m a t e the value of the c o r r e c t i o n

f a c t o r , which i s expressed a s

This c o r r e c t i o n f a c t o r i s dependent upon the degree of a c t u a l

BCF = 0.77 - 1; (2.10)

where

BCF = c o r r e c t i o n f a c t o r f o r s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t a s proposed by Berge l i n , 4

X = b a f f l e spacing ( a s i l l u s t r a t e d i n Fig. 2 .2) , f t , and

Y = r a d i a l d i s t a n c e from cen te r of window t o c e n t e r of opposing window ( a s i l l u s t r a t e d i n Fig. 2 .2 ) , f t .

@ - W I N D O W Z O N E

@ - B A F F L E Z O N E ( P U R E CROSS FLOW)

@ - W I N D O W Z O N E

Fig. 2 .2 . Zones of Flow Between Two B a f f l e s i n the S h e l l Side of the MSBR Primary H e s t Exchanger.

13

I n the method advanced by berg el it^,^ the r eg ion between two b a f f l e s

i s considered a s t h r e e p a r t s : one pure cross-f low zone between two win-

dow zones, a s i l l u s t r a t e d i n Fig. 2 . 2 . The mass velo'city i n each zone

i s based on the e f f e c t i v e a r e a of each zone. I n a window zone, the

e f f e c t i v e a r e a i s given by the expres s ion

(2.11)

where

Sw = f r e e c r o s s - s e c t i o n a l a r e a i n b a f f l e window, ft', and

SB = f r e e c r o s s - s e c t i o n a l a r ea f o r c r o s s flow between tubes appl ied a t l i p of the b a f f l e , f t 2 .

The e f f e c t i v e a r e a of t he pure cross-flow zone i s given by the expres s ion

= 0.5(S + SB2) 'm B 1

(2.12)

where the i n d i c e s 1 and 2 i n d i c a t e the s i d e s of the pure cross-f low zone.

Based on t h i s d e f i n i t i o n of the a r e a s o r zones used t o c a l c u l a t e the mass

v e l o c i t y , the Reynolds number f o r each zone i s determined from the

expres s ion

- - %e - % (2.13)

where

d = o u t s i d e diameter of the tube, f t , 0

G = mass v e l o c i t y of the f l u i d o u t s i d e the tubes , lb/hr . f t ' , and

p,, = v i s c o s i t y a t temperature of bulk f l u i d , l b / h r - f t .

The r e l a t i o n s h i p between the Reynolds number f o r each flow zone and

an appropr i a t e h e a t t r a n s f e r f a c t o r (J) i s developed i n B e r g e l i n ' s meth-

~ d . ~ The h e a t t r a n s f e r f a c t o r f o r t he window zone i s determined from the

expres s ion

h 213 0.14

J w = -(?) C G (%] (EFo)(BCF) (LF) P m

where

h

C = s p e c i f i c h e a t , B t u / l b * " F ,

Gm = mean mass v e l o c i t y of f l u i d , l b / h r - f t 2 ,

= h e a t t r a n s f e r c o e f f i c i e n t f o r window zone, B tu /h r* f t2 . 'F , W

P

(2.14)

14

k = thermal conduc t iv i ty , B t u / h r . f t * " F ,

p,, = v i s c o s i t y a t temperature of bulk f l u i d , l b / h r * f t ,

= v i s c o s i t y of f l u i d a t temperature of w a l l s u r f a c e , l b / h r . f t , % EF = enhancement f a c t o r o u t s i d e h e l i c a l l y indented tube given by

BCF = c o r r e c t i o n f a c t o r f o r s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t

0 Eq. 2 . 2 ,

given by Eq. 2.10, and

LF = leakage f a c t o r f o r h e a t t r a n s f e r taken as 0.8.

The h e a t t r a n s f e r f a c t o r f o r the cross-f low zone (J ) i s determined from

the expres s ion B

213 0.14

(EFo) (BCF) (LF) * (2.15) J B = ? ? - ( hB cppb k ) (:)

P B

Equations 2.16 and 2 . 1 7 were der ived from the graph of J ve r sus NRe given

i n Ref. 4 t o determine the va lues of J . The va lues of 3 determined from

E q s . 2.16 and 2 .17 w e r e then used i n E q s . 2.14 and 2.15 t o determine the

h e a t t r a n s f e r c o e f f i c i e n t s f o r the window zones and the cross-f low zone

(hw and hB) .

(2.16)

(2.17)

For 800 5 NRe 5 lo5 , 3 = 0.346 (NRe) 0 -382

For 100 _< NRe _< 800, J = 0.571(N )0'456 R e

The values of the h e a t t r a n s f e r c o e f f i c i e n t s f o r the window zones (h W l

and h ) and the value f o r the cross-f low zone (h ) were then combined

i n E q . 2.18 t o determine the t o t a l h e a t t r a n s f e r c o e f f i c i e n t f o r t he

region between two b a f f l e s .

w2 B

h t = h a + h a + h a B B WI ~1 w2 w 2

(2.18)

where a = the a r e a of h e a t t r a n s f e r su r f ace i n each zone, f t 2 / f t .

The d a t a r epor t ed by D. A . Donohuelo were used f o r h e a t t r a n s f e r

c a l c u l a t i o n s involving p a r a l l e l flow on the s h e l l s i d e of the MSBR p r i -

mary h e a t exchanger. The h e a t t r a n s f e r c o e f f i c i e n t o u t s i d e the tubes i s

given by the expres s ion

J

d G 0.6 c 1-1 0.33 0.14

(12d ) O * s pb (2.19) 0 = eq (e) ( ko (?)

W

v

15

where

ko = thermal conduc t iv i ty of f l u i d o u t s i d e tubes, B t u / h r . f t . O F ,

do = o u t s i d e diameter of tube, f t ,

eq

vb = v i s c o s i t y a t temperature of

C = s p e c i f i c h e a t , Btu/ lb ."F, and

d = e q u i v a l e n t diameter , f t ,

G = mass v e l o c i t y o f f l u i d ou t s ide tubes , l b / h r . f t 2 ,

bulk f l u i d , l b / h r - f t ,

P = v i s c o s i t y of f l u i d a t temperature of w a l l s u r f a c e , l b / h r - f t .

The o v e r a l l h e a t t r a n s f e r c o e f f i c i e n t was then c a l c u l a t e d by u s i n g the

expres s ion

FrS

1 u = ' 1 1 0 - + - + L(2) ho hw hi di

(2.20)

where ho, $, and h . a r e the s h e l l - s i d e , w a l l , and tube-side h e a t t r a n s -

f e r c o e f f i c i e n t s , r e s p e c t i v e l y . 1

The s h e l l - s i d e p re s su re drops i n the b a f f l e d region of t he MSBR

primary h e a t exchanger were c a l c u l a t e d by us ing the equat ions r epor t ed by

0. P. Be rge l in e t a l . *

given by the expres s ion

The p res su re drop ac ross the cross-f low zone i s

LIPcross flow (2.21)

where

r = number of cross-flow restrictions, B p = d e n s i t y of f l u i d , l b / f t 3 ,

= cross-f low v e l o c i t y of f l u i d (based on e f f e c t i v e a r e a S given m by Eq. 2 .121 , f t / s e c , 'm

gc = dimensional conversion f a c t o r = 32.2 l b m . f t / l b f * s e c 2 ,

PLF = p r e s s u r e drop leakage f a c t o r taken a s 0.5, and

EF = enhancement f a c t o r o u t s i d e h e l i c a l l y indented tubes taken a s 1-30

The p res su re drop a c r o s s the window zone i s given by the expres s ion

(2.22) window LIP

16

where

r = number of r e s t r i c t i o n s i n the window zone and

V = mean flow v e l o c i t y (based on the e f f e c t i v e a r e a S given by W

Z Z E q . 2 . 1 1 ) , f t / s e c .

The number of r e s t r i c t i o n s was i n t e r p r e t e d a s being the number of rows

of tubes i n the d i r e c t i o n of c r o s s flow. The f u l l number was used f o r

the cross-f low zone, while only h a l f of the number of rows was used f o r

each of the window zones. The s h e l l - s i d e p re s su re drop i n the upper

bent- tube r eg ion of the exchanger was taken a s being approximately equa l

t o the p re s su re drop ac ross one b a f f l e d zone.

W

2 . 3 Descript ion of PRIMEX

The computer program f o r the MSBR primary h e a t exchanger, PRIMEX,

i s p re sen ted i n Appendix B. I n t h i s program, each zone between two b a f -

f l e s was considered a s one increment length. The c a l c u l a t i o n s a r e begun

on the h o t s i d e of the h e a t exchanger, and increments a r e added u n t i l a

complete h e a t balance i s achieved. The dependence of each of the physi-

c a l p r o p e r t i e s on temperature i s given a s an empi r i ca l equa t ion , and

these equa t ions a r e inco rpora t ed i n the main program. I f any of these

equa t ions a r e changed, the appropr i a t e d a t a ca rd must be r ep laced . The

phys ica l p rope r ty d a t a a s w e l l a s the o t h e r i npu t d a t a r equ i r ed f o r the

PRIMEX program a r e l i s t e d i n Appendix B . A l i s t of the ou tpu t d a t a

received from the computer i s a l s o p re sen ted .

A s t r e s s a n a l y s i s sub rou t ine , TUBSTR, i s inco rpora t ed i n the main

program. This subrout ine performs a p re l imina ry stress a n a l y s i s of the

tubes w i t h the assumption t h a t the maximum tube s t ress w i l l occur i n the

upper bent- tube r eg ion of the h e a t exchanger. Pressure s t r e s s e s , stresses

r e s u l t i n g from thermal expansion, and stresses r e s u l t i n g from the thermal

g r a d i e n t ac ross the tube w a l l a r e considered. The primary and secondary

s t r e s s e s a r e computed, and these computed va lues a r e compared wi th the

al lowable values given i n Sec t ion 111, Nuclear Vessels, of the ASME

B o i l e r and Pressure Vessel Code. A second subrou t ine , LAGR, i s used f o r

17

U i n t e r p o l a t i o n of values from a given t a b l e . The complete l i s t i n g f o r the

main program toge the r with i t s two subrou t ines i s given i n Appendix B .

To i l l u s t r a t e the use of the PRIMEX program, the computer i npu t d a t a

f o r the MSBR primary h e a t exchanger discussed i n Subsection 2 . 1 and the

ou tpu t d a t a p r i n t e d by the computer a r e included i n Appendix B . The time

r equ i r ed f o r a t y p i c a l IBM 360/91 computer run of t h i s program i s about

2 minutes.

2.4 Evaluat ion of PRIMEX

It i s b e l i e v e d t h a t the use of the PRIMEX computer program w i l l

r e s u l t i n a primary h e a t exchanger whose volume of f u e l s a l t w i l l be kept

t o a minimum and whose design w i l l be more r e l i a b l e than can be achieved

wi th normal hand c a l c u l a t i o n s . Var i a t ions i n phys i ca l p r o p e r t i e s and

complicated geometries a r e handled e a s i l y , and an ex tens ive parameter

s tudy can be made i n a very s h o r t t i m e .

However, t he output of a computer program cannot be b e t t e r than the

i n p u t . The inpu t d a t a which have a s i g n i f i c a n t e f f e c t on the design of

the h e a t exchanger a r e the phys ica l p r o p e r t i e s of the f u e l and coolant

s a l t s , the h e a t t r a n s f e r c o r r e l a t i o n s used, the enhancement f a c t o r s

assumed f o r the h e l i c a l l y indented tubes , and the leakage f a c t o r s a s s o c i -

a t ed wi th f a b r i c a t i o n c l ea rances . The average d e v i a t i o n s i n the phys ica l

p r o p e r t i e s of t he f u e l and coo lan t s a l t s p r e s e n t l y used i n the program

a r e those r epor t ed by J. R. McWherter.”

i n the phys ica l p rope r ty va lues p r e s e n t l y a r e a s soc ia t ed wi th the v i scos -

i t y and thermal conduc t iv i ty of the f u e l s a l t . The average d e v i a t i o n

f o r the f u e l - s a l t h e a t t r a n s f e r c o r r e l a t i o n i s reported6 a s being about

5.7%. The d e v i a t i o n o r e r r o r r e s u l t i n g from the use of Be rge l in ’ s cor-

r e l a t i o n 4 i s no t c e r t a i n , b u t s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t s nor-

mally have a d e v i a t i o n of about 25%. The leakage f a c t o r d e v i a t i o n f o r

the p re s su re drop might be about 20%, and the leakage f a c t o r d e v i a t i o n

f o r the s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t might be about 10%. The

enhancement f a c t o r d e v i a t i o n might be about 15%.

The most no tab le u n c e r t a i n t i e s

18

The two extreme cases w e r e checked. A l l of the p e s s i m i s t i c values

were used i n one case , and a l l of the o p t i m i s t i c values were used i n the

o t h e r case . The r e s u l t was a maximum es t ima ted d e v i a t i o n i n the o v e r a l l

h e a t t r a n s f e r a r e a (or volume of f u e l s a l t ) of +38% ( a d d i t i o n a l a r e a

r equ i r ed ) f o r the p e s s i m i s t i c case and -28% ( l e s s a r e a r e q u i r e d ) f o r the

o p t i m i s t i c case.

19

3 . RETEX, THE STEAM REHEATER EXCHANGER PROGRAM

The coolant s a l t c i r c u l a t i n g system i n the conceptual design of a

s i n g l e - f l u i d MSBR c o n s i s t s of fou r independent loops, each con ta in ing

s a l t c i r c u l a t i n g pumps, steam gene ra to r s , steam r e h e a t e r s , and the s h e l l

s i d e of one of t he fou r primary h e a t exchangers. There a r e two steam

r e h e a t e r exchangers, which t r a n s f e r h e a t from the coolant s a l t t o pre-

hea ted exhaust steam from the high-pressure t u r b i n e , i n each coo lan t s a l t

loop; w i th a t o t a l o f e i g h t r e h e a t e r s t o meet the t o t a l steam r e h e a t i n g

requirement of approximately 5.1 X 10" lb /h r .

same des ign , and each has a thermal capac i ty of about 36.6 MW.

Each r e h e a t e r i s of the

A t f u l l design load, the coolant s a l t from the primary h e a t exchanger

e n t e r s the s h e l l s i d e of the r e h e a t e r a t a temperature of 1150°F and

e x i t s a t a temperature of 850°F f o r r e t u r n t o the primary h e a t exchanger.

The preheated exhaust steam from the high-pressure tu rb ine e n t e r s the

tube s i d e of t he r e h e a t e r a t a temperature of 650"F, flows through the

tubes i n counterflow t o the coolant s a l t , and leaves the r e h e a t e r a t a

temperature of 1000°F f o r d e l i v e r y t o the in t e rmed ia t e -p res su re tu rb ine .

B a s i c a l l y , the steam r e h e a t e r exchangers must m e e t the same system

requirements p r e s c r i b e d f o r the primary h e a t exchangers t h a t w e r e d i s -

cussed i n Sec t ion 2 of t h i s r e p o r t . However, s i n c e no f u e l s a l t i s

involved, the d e s i r a b i l i t y of keeping the f l u i d volume a t a minimum i s

n o t a c r i t i c a l f a c t o r i n the design of the r e h e a t e r . I n a d d i t i o n , the

lower h e a t load and average temperatures permit more freedom i n designing

the geometry of the r e h e a t e r t o avoid problems a s soc ia t ed with v i b r a t i o n

o r o v e r s t r e s s . '

Since the design f o r t he steam r e h e a t e r exchanger i s s i m i l a r t o

t h a t f o r the primary h e a t exchanger, an e a r l y ve r s ion of the b a s i c PRIMEX

computer program was modified t o f i t the requirements of the steam

r e h e a t e r , thereby becoming the RETEX program.

t i o n s used t o develop the RETEX computer program a r e discussed i n the

fol lowing subsec t ions .

The design d a t a and equa-

20

3 . 1 Descr ipt ion of Steam Reheater

Each of the e i g h t steam r e h e a t e r exchangers i s a h o r i z o n t a l s h e l l -

and-tube u n i t w i th a s i n g l e counterflow pass on both the s h e l l and tube

s i d e s . Each u n i t i s about 30 f t long and has an o u t s i d e diameter of

22 i n . A t y p i c a l r e h e a t e r i s i l l u s t r a t e d i n Fig. 3.1.

The preheated exhaust steam e n t e r s the tube s i d e of the r e h e a t e r a t

a p re s su re of about 580 p s i , flows through the 0.75-in.-OD tubes , and

e x i t s a t a p re s su re of 550 p s i . There a r e 400 s t r a i g h t tubes arranged

i n a t r i a n g u l a r - p i t c h a r r a y i n each r e h e a t e r . The s u r f a c e s of these

tubes a r e n o t h e l i c a l l y indented t o enhance h e a t t r a n s f e r , a s a r e those

i n the primary h e a t exchanger.

The coolant s a l t e n t e r s the s h e l l s i d e of t he r e h e a t e r a t a p re s su re

of about 228 p s i , flows around d i s k and doughnut b a f f l e s i n counterflow

t o the exhaust steam, and e x i t s a t a p re s su re of 168 p s i . Other p e r t i -

nent design d a t a f o r the steam r e h e a t e r exchanger a r e given i n Table 3.1.

Table 3.1. Design Data f o r MSBR Steam Reheater Exchanger

Number r equ i r ed

Rate of h e a t t r a n s f e r p e r u n i t , Mw B t u / h r

She l l - s i d e cond i t ions Hot f l u i d Entrance temperature , "F E x i t temperature, "F Entrance p r e s s u r e , p s i E x i t p r e s s u r e , p s i Pressure drop ac ross exchanger, p s i Mass flow r a t e , l b / h r

Cold f l u i d Entrance temperature, "F E x i t temperature , "F Entrance p r e s s u r e , p s i E x i t p r e s s u r e , p s i Pressure drop ac ross exchanger, p s i Mass flow r a t e , l b / h r

Tube-side cond i t ions

S t r a i g h t shel l -and-tube one-pass h o r i z o n t a l u n i t w i th d i s k and doughnut b a f f l e s

Eight

36.6 1.25 X lo8

Coolant s a l t 1150 850 228 168 59.52 1.16 X lo6

Exhau s t s te am 650 1000 580 550 29.85 6.41 x io5

2 1

ORNL Dwg 65 12381 - STEAM OUTLET

SALT INLET

T U B U L A R S H E L L

DOUGHNUT - BAFFLE

INSULATION BAFFLE-

-

-“TUBE SHEET

-T IE ROD 8 SPACER

-TUBES

-DISC B

----SA

AFF

, L T

:LE

ou TL

- ‘ - -STEAM I N L E T 1.

E T

Fig. 3.1. Typical MSBR Steam Reheater Exchanger.

22

Table 3 . 1 (continued)

Tub e Mater ia 1 Has te l loy N Number r equ i r ed 400 P i t c h , i n . 1.0 ( t r i a n g u l a r ) Outside diameter , i n . 0.75 Wall t h i ckness , i n . 0.035 Length (tube s h e e t t o tube sheet) , f t 30.26

Tube s h e e t m a t e r i a l Has t e l loy N Tota l h e a t t r a n s f e r a r e a , f t 2 2376

Basis f o r a r e a c a l c u l a t i o n Outside of tubes

She 11 Materia 1 Thickness, i n . In s ide diameter , i n .

Has t e l loy N 0.5 21 .2

B a f f l e Type Number 2 1 each Spacing, i n . 8 .65 Disk o u t s i d e diameter , i n . 17.75 Doughnut i n s i d e diameter , i n . 11.61

Btu/hr f t2 306

Disk and doughnut

Overal l h e a t t r a n s f e r c o e f f i c i e n t , U ,

Tube Maximum primary (P,) s t r e s s

Ca lcu la t ed , p s i 4582 A 1 lowab l e , p s i 13 , 000

Maximum primary and secondary (Pm + Q) s t r e s s

Ca lcu la t ed , p s i 14 , 090 Allowable , p s i 39 , 000

S h e l l Maximum primary (Pm> s t ress

Ca lcu la t ed , p s i 5016 Allowable , p s i 9500

Maximum primary and secondary (Pm + Q) stress

Ca lcu la t ed , p s i 14 , 550 Allowable, p s i 28 , 500

23

3 . 2 Design Ca lcu la t ions

When developing the computer program RETEX t o analyze the steam

r e h e a t e r exchanger, the p r o p e r t i e s of the steam were assumed t o be essen-

t i a l l y cons t an t along the l eng th of the exchanger even though i t was

recognized t h a t some ga in i n the r e l i a b i l i t y of the e s t i m a t e s could have

been r e a l i z e d by inco rpora t ing the steam p r o p e r t i e s a s a func t ion o f

p r e s s u r e and temperature. The usua l D i t tu s -Boe l t e r equa t ions were used

f o r the f i l m h e a t t r a n s f e r c o e f f i c i e n t on the tube s i d e of the exchanger.

The o t h e r procedures and c o r r e l a t i o n s used i n the a n a l y s i s of the r e h e a t e r

a r e b a s i c a l l y the same a s those used f o r the primary h e a t exchanger d i s -

cussed i n Subsect ion 2 . 2 of t h i s r e p o r t .

Manual computational methods were used t o determine the stresses

i n the steam r e h e a t e r exchanger. This prel iminary s t r e s s a n a l y s i s was

based on the requirements of Sec t ion 111, Nuclear Vessels, of the ASME

B o i l e r and P res su re Vessel Code; and the c a l c u l a t e d va lues a r e compared

w i t h t h e al lowable va lues i n Table 3.1. However, a complete stress

a n a l y s i s a s r equ i r ed by Sec t ion I11 of the ASME B o i l e r and Pressure Ves-

s e l Code has n o t been made.

3 . 3 Descript ion of RETEX

The RETEX program, a modified v e r s i o n of t he PRIMEX program, was

used t o analyze the steam r e h e a t e r exchanger. I n the RETEX program, each

zone between two b a f f l e s i s considered a s one increment length. The c a l -

c u l a t i o n s a r e begun on the h o t s i d e of the exchanger, and increments a r e

added u n t i l a complete h e a t balance i s achieved. The p h y s i c a l p rope r ty

equat ions f o r t he f u e l s a l t i n the PRIMEX program a r e replaced wi th the

p h y s i c a l p rope r ty d a t a f o r the exhaust steam i n the RETEX program, and

these p r o p e r t i e s a r e considered a s being e s s e n t i a l l y cons t an t along the

l eng th of the exchanger. The phys ica l p r o p e r t i e s of the coolant s a l t a r e

eva lua ted a t the average temperature of each increment. The dependence.

of the p h y s i c a l p r o p e r t i e s on temperature i s p r e s e n t l y expressed i n the

24

form of empi r i ca l equa t ions incorporated i n the main program. I f any of

these equat ions a r e changed, the appropr i a t e d a t a card must be replaced.

The RETEX computer program d i f f e r s from the PRIMEX computer program

i n t h a t

1. the r e h e a t e r tubes a r e no t h e l i c a l l y indented t o enhance h e a t t r a n s -

f e r , and no enhancement f a c t o r s a r e used i n the RETEX program;

2. the r e h e a t e r tubes a r e arranged i n a t r i a n g u l a r - p i t c h a r r a y r a t h e r

than i n concen t r i c c i r c l e s , and c e r t a i n geometric c a l c u l a t i o n s a r e

t h e r e f o r e made d i f f e r e n t l y i n the RETEX program;

3 . none of the r e h e a t e r tubes a r e ben t i n a sine-wave conf igu ra t ion t o

accommodate d i f f e r e n t i a l thermal expansion; and

4 . no s t ress a n a l y s i s sub rou t ines a r e included i n the RETEX program

( s t r e s s e s were c a l c u l a t e d by hand).

The computer program f o r the MSBR steam r e h e a t e r exchanger, RETEX,

i s given i n Appendix C. A s i m p l i f i e d o u t l i n e of the program i n block-

diagram form, a l i s t of the inpu t d a t a r equ i r ed , a l i s t of t he output

r ece ived from the computer, and a complete l i s t i n g of the main program

a r e presented. The RETEX program terms which d i f f e r from those of t he

PRIMEX program a r e def ined. T o i l l u s t r a t e the use of the RETEX program,

the computer i n p u t da t a f o r the steam r e h e a t e r exchanger discussed i n

Subsection 3 . 1 and the output p r i n t e d by the computer a r e a l s o included

i n Appendix C. The t i m e r equ i r ed f o r a t y p i c a l IBM 3 6 0 / 9 1 computer run

of t h i s program i s about 1 minute.

3.4 Evaluat ion of RETEX

Confidence i n the design c a l c u l a t i o n s f o r the steam r e h e a t e r

exchanger i s g r e a t e r than t h a t i n the c a l c u l a t i o n s f o r the primary h e a t

exchanger because the c h a r a c t e r i s t i c s of steam a r e more f a m i l i a r than

those of the f u e l s a l t and because no enhancement f a c t o r s a r e involved.

Vibrat ion problems a r e no t l i k e l y t o be encountered i n the steam r e h e a t e r

because v e l o c i t i e s a r e less than 6.5 f p s and the tubes a r e supported by

b a f f l e s w i th a r e l a t i v e l y c l o s e spacing.

25

V The u n c e r t a i n t i e s a s soc ia t ed wi th the coo lan t s a l t a r e involved i n

the RETEX program, and the dev ia t ions app l i ed f o r the primary h e a t

exchanger (discussed i n Subsection 2.4) a r e a l s o a p p l i c a b l e t o the steam

r e h e a t e r . Again, two extreme cases were considered. A l l the p e s s i m i s t i c

va lues were used i n one case , and a l l the o p t i m i s t i c values were used i n

the o t h e r . The r e s u l t was a maximum es t ima ted d e v i a t i o n i n the o v e r a l l

h e a t t r a n s f e r a r e a of +23% ( a d d i t i o n a l area r e q u i r e d ) f o r t h e p e s s i m i s t i c

case and -13% (less a r e a r equ i r ed ) f o r the o p t i m i s t i c case.

4 . SUPEX, THE STEAM GENERATOR SUPERHEATER PROGRAM

There a r e fou r steam gene ra to r supe rhea te r exchangers, which t r a n s f e r

h e a t from the coolant s a l t t o feedwater, i n each of the fou r coolant s a l t

c i r c u l a t i n g loops of the MSBR concept. The t o t a l steam gene ra t ion r equ i r e -

ment, which inc ludes t h a t needed f o r the feedwater and p rehea t ing the

exhaust steam, of about 10 X lo6 l b / h r i s provided by the 16 steam gener-

a t o r s , each having a thermal capac i ty of about 1 2 1 MW.

These exchangers s e rve a s both steam gene ra to r s and supe rhea te r s .

They a r e operated i n p a r a l l e l w i th r e s p e c t t o the coo lan t s a l t and steam

flows, and they a r e i d e n t i c a l i n design and ope ra t ion .

l oad , preheated feedwater e n t e r s the exchanger a t a temperature of 700"F,

and the s u p e r c r i t i c a l steam e x i t s a t a temperature of 1000°F. The cool-

a n t s a l t e n t e r s the exchanger a t a temperature of 1150°F and e x i t s a t a

temperature of 850°F f o r r e t u r n t o the primary h e a t exchanger.

A t f u l l design

The f a c t o r s i n f luenc ing the design of the steam gene ra to r exchanger

a r e p a r t i a l l y dependent upon the requirements f o r the o v e r a l l MSBR system.

The e x i t temperature and p res su re of the steam were d i c t a t e d by the steam

power system s e l e c t e d . The i n l e t temperature of the steam was determined

by cons ide ra t ions r e l a t i v e t o the l i qu idus temperature of the s a l t and

the r a p i d inc rease i n h e a t capac i ty of the s u p e r c r i t i c a l water a t temper-

a t u r e s above 700°F. The i n l e t and e x i t temperatures of the coo lan t s a l t ,

the p re s su re drop, and the t o t a l h e a t t o be t r a n s f e r r e d were d i c t a t e d by

the requirements f o r the r e a c t o r and primary h e a t exchange systems.

a d d i t i o n t o these system requirements , the design f o r the steam gene ra to r

exchanger m u s t s a t i s f y s t ress , s t a b i l i t y , and space requirements .

I n

Because of the marked changes i n the phys ica l p r o p e r t i e s o f the feed-

water a s the temperature i s r a i s e d above the c r i t i c a l temperature a t

s u p e r c r i t i c a l p r e s s u r e s , the h e a t t r a n s f e r and flow c h a r a c t e r i s t i c s vary

considerably throughout the exchanger. The SUPEX computer program was

developed t o account f o r these changes by making the h e a t t r a n s f e r and

p res su re drop c a l c u l a t i o n s f o r incremental tube l eng ths . The design d a t a

and equat ions used t o develop t h i s computer program f o r a n a l y s i s of the

steam gene ra to r exchanger a r e discussed i n the fol lowing subsec t ions .

V

27

4.1 Descr ipt ion of Steam Generator

W

Each of the 16 steam gene ra to r supe rhea te r exchangers i s a U-tube,

U-shel l u n i t mounted h o r i z o n t a l l y wi th one l e g above the o t h e r . Each has

a s i n g l e pass on the s h e l l and tube s i d e s wi th the flow i n one s i d e coun-

ter t o t h a t i n the o t h e r .

40 f t , and the o v e r a l l h e i g h t from the feedwater i n l e t plenum t o the

steam o u t l e t plenum i s about 1 2 f t .

i n Fig. 4.1.

The o v e r a l l l eng th of each exchanger i s about

A t y p i c a l steam gene ra to r i s shown

ORNL-DWG 70-11951

STEAM OUTLET

4

i i

4 FEEDWATER

INLET

Fig . 4.1. Typical MSBR Steam Generator Superheater Exchanger.

28

\

The feedwater e n t e r s the tube s i d e of the exchanger a t a p re s su re

of 3754 p s i , flows through the 0.50-in.-OD tubes, and the s u p e r c r i t i c a l

steam e x i t s a t a p re s su re of 3600 p s i . The coolant s a l t e n t e r s the s h e l l

s i d e of the exchanger a t a p re s su re of 233 p s i , c i r c u l a t e s i n counterflow

t o the s u p e r c r i t i c a l f l u i d around segmental b a f f l e s , and e x i t s a t a p re s -

su re of 1 7 2 p s i . Segmental b a f f l e s a r e used t o improve the h e a t t r a n s f e r

c o e f f i c i e n t f o r the s a l t f i l m and t o minimize s a l t s t r a t i f i c a t i o n . A

b a f f l e on the s h e l l s i d e of each tube s h e e t provides a s t agnan t l a y e r of

s a l t t o h e l p reduce stresses r e s u l t i n g from temperature g r a d i e n t s ac ross

the tube s h e e t s . Location o f the steam gene ra to r exchanger i n a h o r i z o n t a l p o s i t i o n

reduces the p o s s i b i l i t y of uns t ab le flow cond i t ions f o r the s u p e r c r i t i c a l

f l u i d i n the tubes. The U-tubes a r e arranged i n a t r i a n g u l a r - p i t c h a r r a y

and the ends of the tubes are turned 90" t o e q u a l i z e the l eng ths of t he

tubes i n the exchanger. This e q u a l i z a t i o n of tube l eng ths f u r t h e r

reduces the p o s s i b i l i t y of u n s t a b l e flow cond i t ions . The p e r t i n e n t

design d a t a f o r the steam gene ra to r exchanger a r e given i n Table 4.1.

Table 4.1. Design Data f o r MSBR Steam Generator Superheater Exchanger

U-she l l , U-tube one-pass h o r i - z o n t a l u n i t w i th cross-f low b a f f l e s

TYP e

Number r equ i r ed 16

Rate of h e a t t r a n s f e r p e r u n i t , Mw 1 2 1 B t u /h r 4.13 X lo8

S h e l l - s i d e cond i t ions H o t f l u i d Coolant s a l t Entrance temperature, O F 1150 Exit temperature, "F 850 Entrance p r e s s u r e , p s i 233.0 E x i t p r e s s u r e , p s i 172.0 Pressure drop ac ross exchanger, p s i 61.0 Mass flow r a t e , l b / h r 3.82 X lo6

U

29

v Table 4 .1 (cont inued)

Tube-side cond i t ions Cold f l u i d Entrance temperature , OF E x i t temperature , "F Entrance p r e s s u r e , p s i E x i t p r e s s u r e , p s i Pressure drop ac ross exchanger, p s i Mass flow r a t e , l b / h r Mass v e l o c i t y , l b / h r - f t 2

Mater ia 1 Number r equ i r ed P i t c h , i n . Outside diameter , i n . Wall t h i c k n e s s , i n . Length (tube s h e e t t o tube sheet) , f t

Tube s h e e t Mate r i a 1 Thickness, i n .

To ta l h e a t t r a n s f e r a r e a , f t 2 Basis f o r a r e a c a l c u l a t i o n

She 11

Tube

Mate r i a l Wall t h i ckness , i n . I n s i d e diameter , i n .

B a f f l e Type Spacing, f t Number of spaces

S u p e r c r i t i c a l f l u i d 700 1000 3754 3 600 154 6.33 x io5 2.47 x lo6

Has te l loy N 393 0.875 ( t r i a n g u l a r ) 0.50 0.077 76.4

Has te l loy N 4.5

3929 Outside of tubes

Has te l loy N 0.375 18.25

Cross flow 4.02 19

4.2 Design Ca lcu la t ions

The h e a t t r a n s f e r c o e f f i c i e n t f o r the s u p e r c r i t i c a l f l u i d f i l m on

the i n s i d e of t he tube w a l l s i s determined by u s i n g the c o r r e l a t i o n

r epor t ed by H. S . Swenson e t a1.12 This c o r r e l a t i o n i s given i n Eq. 4.1.

30

W

where

h . = h e a t t r a n s f e r c o e f f i c i e n t i n s i d e tube, Btu/hr . f t2SoF,

d . = i n s i d e diameter of tube , f t ,

k i = thermal conduc t iv i ty o f f l u i d i n s i d e tube, Btu/hr . f t2*OF pe r f t ,

G = mass v e l o c i t y of f l u i d , l b / h r * f t 2 ,

1

1

pi = v i s c o s i t y of f l u i d a t temperature of i n s i d e s u r f a c e o f tube ,

Hi = en tha lpy a t temperature o f i n s i d e s u r f a c e of tube , B tu / lb ,

% = en tha lpy a t temperature of bu lk f l u i d , Btu / lb ,

Ti = temperature of f l u i d a t i n s i d e s u r f a c e o f tube , OF,

T = temperature of bu lk f l u i d , OF,

v = s p e c i f i c volume of bu lk f l u i d , f t 3 / l b , and

v = s p e c i f i c volume of f l u i d i n s i d e tube , f t 3 / l b .

l b /h r . f t ,

b

b

i

The va lues o f s p e c i f i c volume and en tha lpy f o r t h e s u p e r c r i t i c a l f l u i d

under va r ious cond i t ions of p re s su re and temperature a r e taken from d a t a

r epor t ed by J . H. Kennan and F. G. Keyes.13

i s inc luded i n the SUPEX computer program f o r de te rmina t ion o f t hese

va lues . The va lues of thermal conduc t iv i ty and v i s c o s i t y f o r t he super-

A t a b l e look-up subrout ine

c r i t i c a l f l u i d a r e determined from d a t a r epor t ed by E. s . Nowak

R. J . Grosh.14 These d a t a were represented by E q s . 4.2 and 4.3

SUPEX computer program.

V T + 460 ' = 0*02191(v - 0.012)2( 492

and

T t4::46-)

k = (1.093 X (T + 460)1'45 + (28.54 X 10-4)v-1*25,

where

v = s p e c i f i c volume, f t " / l b , and

T = temperature o f f l u i d , "F.

and

i n the

(4 .2 )

(4 .3 )

The h e a t t r a n s f e r c o e f f i c i e n t f o r the s a l t f i l m on the o u t s i d e s u r -

f ace of the tubes i s determined by us ing the method proposed by 0. P.

Berge l in e t a l . 4 ' 5

between a h e a t t r a n s f e r f a c t o r (J) and the Reynolds number, w i th the

Reynolds number def ined by the express ion

The experimental da ta4 a r e presented a s c o r r e l a t i o n s

31

d G 0

N& pb E-

where

d = o u t s i d e diameter of tube, f t ,

G = mass v e l o c i t y of the f l u i d , l b / h r . f t 2 , and 0

pb = v i s c o s i t y a t temperature of bulk f l u i d , l b / h r * f t .

The shel l s i d e of the steam gene ra to r exchanger i s divided i n t o two types

of flow regions by the segmental b a f f l e s . These a r e the cross-f low and

window reg ions , and the h e a t t r a n s f e r f a c t o r i s determined f o r each. The

h e a t t r a n s f e r f a c t o r f o r the cross-f low reg ion (JB) i s given by the

expres s ion

h 2/3 0.14 - B Pl-b

JB -=('k P B ) (:) ( 4 . 5 )

where

hB = h e a t t r a n s f e r c o e f f i c i e n t f o r cross-f low reg ion , B tu /h r . f t2 . O F ,

C = s p e c i f i c h e a t , Btu/ lb ."F,

GB = mass v e l o c i t y of f l u i d i n cross-flow reg ion , l b / h r . f t 2 ,

% = v i s c o s i t y a t temperature of bulk f l u i d , l b / h r . f t ,

P

k = thermal conduc t iv i ty , B t u / h r * f t - " F , and

= v i s c o s i t y of f l u i d a t temperature of o u t s i d e su r face of tube, l b / h r . f t .

The h e a t t r a n s f e r f a c t o r f o r the window reg ion i s given by the expres s ion

where

h

Gm = mean mass v e l o c i t y , l b / h r . f t 2 .

= h e a t t r a n s f e r c o e f f i c i e n t f o r window reg ion , B t u / h r . f t 2 . O F , and W

The mean mass v e l o c i t y i s given by the expression

where Gw = mass v e l o c i t y of f l u i d i n window reg ion , l b / h r - f t 2 .

f o r determining values of J were f i t t e d t o the graph of J ve r sus NRe

given i n Fig. 11 of Ref. 4 f o r u se i n the SUPEX computer program. The

Equations

3 2

va lues of J given by E q s . 4.8 and 4.9 a r e used i n Eqs. 4 .5 and 4.6 t o

determine the h e a t t r a n s f e r c o e f f i c i e n t s f o r the cross-f low and window

regions (hB and hw).

For 100 5 NRe ,< 800, J = 0.571(NR,)-0*456 ( 4 - 8 ) and

For 800 _< NRe 5 lo5, J = 0.346(NRe)-0'382 (4.9)

I n Berge l in ' s methodY4 the h e a t t r a n s f e r c o e f f i c i e n t f o r the s h e l l s i d e

of the exchanger i s a l i n e a r combination of the h e a t t r a n s f e r c o e f f i c i e n t s

f o r the cross-f low and window regions weighted by the amount of h e a t

t r a n s f e r su r f ace i n each region and co r rec t ed f o r bypass leakage.

Because of the l a rge baffle-spacing-to-shell-diameter r a t i o (approximately

2 .7) r equ i r ed f o r the steam gene ra to r exchanger, an a d d i t i o n a l c o r r e c t i o n

f a c t o r i s app l i ed t o the s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t . The t o t a l

s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t (h ) i s given by the expres s ion 0

where

B =

Y =

x = h = B a = B

h =

a = W

W

The

s a l t a r e

included

0.138 hgag + hwaw)

ho = 0.77B( $1 ( a + a 9 B w (4.10)

bypass leakage f a c t o r recommended by Berge l in , 4

d i s t a n c e from the c e n t e r l i n e of the s h e l l t o t he c e n t r o i d of the segmental window a r e a , f t ,

b a f f l e spacing, f t ,

h e a t t r a n s f e r c o e f f i c i e n t f o r cross-f low reg ion , Btu/hr . f t2-OF,

a r e a of h e a t t r a n s f e r su r f ace i n cross-f low region p e r u n i t l eng th , f t 2 / f t ,

h e a t t r a n s f e r c o e f f i c i e n t f o r window reg ion , B t u / h r . f t 2 . OF, and

a r e a of h e a t t r a n s f e r su r f ace i n window region p e r u n i t l eng th , f t 2 / f t . va lues of s p e c i f i c h e a t and thermal conduc t iv i ty f o r the coo lan t

t r e a t e d a s c o n s t a n t s , independent of temperature, and a r e

i n the inpu t information f o r the SUPEX computer program. The

d e n s i t y and v i s c o s i t y of the s a l t a r e t r e a t e d a s func t ions of temperature

a s determined by Eqs. 4.11 and 4.12.

33

= 141.38 - 0.02466(T)

and

1-1 = 0.2122 exp [ ( : ~ t ~ ~ ) ] ,

(4.11)

(4.12)

where

p = d e n s i t y of coolant s a l t , l b / f t 3 ,

T = temperature of s a l t , OF, and

II = v i s c o s i t y of s a l t , l b / h r - f t .

The thermal r e s i s t a n c e of the tube w a l l i s c a l c u l a t e d f o r each

increment of tube l eng th by us ing the thermal conduc t iv i ty of Has te l loy N

eva lua ted a t the average temperature of the tube w a l l f o r each p a r t i c u l a r

increment.

exp res s ion

The thermal r e s i s t a n c e of the tube w a l l i s given by the

(4.13)

where

% = thermal r e s i s t a n c e of tube w a l l , h r - f t2 -OF/Btu ,

d = ou t s ide diameter of tube, f t ,

$ = thermal conduc t iv i ty of tube w a l l , B t u / h r * f t . " F , and

d. = i n s i d e diameter of tube, f t .

0

1

The thermal conduc t iv i ty of the tube w a l l i s given by the expres s ion

$ = 0.006375Tw + 4.06 (4.14)

where Tw = mean temperature of the tube w a l l , OF. The t o t a l thermal

r e s i s t a n c e , based on the o u t e r su r f ace a r e a of the tube, i s given by the

expre s s i o n

d (4.15)

The h e a t t r a n s f e r r e d p e r increment of exchanger l eng th (AQ) i s given by

the expres s ion

(4.16)

34

where

d = o u t s i d e diameter of tube, f t , 0

n = number of t ubes ,

fi = increment of tube l eng th , f t ,

AT = mean temperature d i f f e r e n c e between coolant s a l t and super- c r i t i c a l f l u i d f o r the p a r t i c u l a r increment, O F , and m

R = t o t a l thermal r e s i s t a n c e given by Eq. 4.15. t

The p res su re drop p e r increment of tube l eng th f o r the s u p e r c r i t i c a l

f l u i d i n s i d e the tubes i s given by the expres s ion

4 f ( f i ) 3 A P = 144di (2gcP) , (4.17)

where

f = f r i c t i o n f a c t o r ,

AL = increment of tube l eng th , f t ,

di

gc = g r a v i t a t i o n a l conversion c o n s t a n t , l b - f t / l b f . h r 2 , and

= i n s i d e diameter of tube, f t ,

G = mass v e l o c i t y of f l u i d i n s i d e tube, l b / h r - f t * ,

m

The f r i c t i o n f a c t o r i s given by the expression*

p = d e n s i t y of f l u i d i n s i d e tube, l b / f t 3 .

f = 0.00140 i- 0.125 (;;G)0'32 - . (4 .18)

The p res su re drops on the s h e l l s i d e of the steam gene ra to r exchanger

a r e c a l c u l a t e d by us ing the equat ions recomended by B e r g e l i x ~ . ~

p res su re drop ac ross the i - t h cross-f low region i s given by the expres s ion

The

(4.19)

where

r = number of r e s t r i c t i o n s i n cross-f low reg ion ,

G B

B p = d e n s i t y of f l u i d , l b / f t 3 .

= mass v e l o c i t y of f l u i d i n cross-f low reg ion , l b / h r . f t 2 , and

35

The p res su re drop ac ross the i - t h b a f f l e window i s given by the

expres s ion

V

144 n e =

wi ( 4 . 2 0 )

where

r = number of r e s t r i c t i o n s i n window reg ion and

G W

= mean mass v e l o c i t y (given by E q . 4 . 7 ) , l b / h r * f t 2 . m

The t o t a l p re s su re drop on the s h e l l s i d e of the exchanger i s given by

the expres s ion

m~ = P 1 mBi -k O w i ) ' i=l i=l

(4.21)

where

B = bypass leakage c o r r e c t i o n f a c t o r f o r p re s su re recommended by Bergelin4 and

N = number of b a f f l e s .

Detai led s t r e s s c a l c u l a t i o n s a r e no t included i n the SUPEX computer

program, b u t an approximate value of the allowable temperature drop ac ross

the tube w a l l based on thermal stress cons ide ra t ions i s determined f o r

each increment of tube l eng th . This value of allowable temperature drop

can be compared wi th the value of the temperature drop ac ross the tube

w a l l determined i n the h e a t t r a n s f e r c a l c u l a t i o n s t o provide some guid-

ance i n s e l e c t i n g design parameters. The thermal s t r e s s e s a r e t r e a t e d

a s secondary stresses. Based on the requirements s e t f o r t h i n Sec t ion

111, Nuclear Vessels, of the ASME B o i l e r and Pressure Vessel Code; the

pe rmis s ib l e value f o r the thermal stresses i s given by the expression

= 3 s - s , (4.22) - AT"h - AT"L m

where

= hoop and l o n g i t u d i n a l stress components caused by temper- a t u r e d i f f e r e n c e s ac ross the tube w a l l , p s i ,

Sec t ion I11 of the ASME B o i l e r and Pressure Vessel Code, p s i , and

AT"h ' AT"L

S = allowable stress i n t e n s i t y based on r u l e s p re sc r ibed i n m

36

S = t o t a l s t ress i n t e n s i t y r e s u l t i n g from primary membrane stresses p l u s secondary stresses from a l l sources o t h e r than thermal stresses, p s i .

The va lue o f S was conse rva t ive ly es t imated t o be about 26,000 p s i . The

tube wa l l m a t e r i a l i s Has te l loy N , and

f o r T, < 1015"F, Sm = 24,000 - 7.5(Tw) (4.23)

and

f o r 1015°F - < T, - < 1100"F, S = 57,000 - 40(Tw) . (4.24) m

Based on d a t a r epor t ed by J. F. Harvey,15 the hoop and l o n g i t u d i n a l

stresses r e s u l t i n g from temperature d i f f e r e n c e s ac ross the tube w a l l a r e

given by the express ion

where

2 = c o e f f i c i e n t of thermal expansion, in . / in . -OF,

E = modulus of e l a s t i c i t y f o r Has te l loy N , p s i ,

ATw = temperature drop ac ross tube w a l l , O F ,

v = Poisson 's r a t i o ,

d = o u t s i d e diameter of tube , i n . , and

di

0

= i n s i d e diameter of tube, i n .

The es t imated va lue of S and E q s . 4.22, 4.23, 4.24, and 4.25 a r e used i n

the SUPEX computer program t o c a l c u l a t e t he al lowable va lue of AT,. The

va lues of E and Q a r e determined i n t h e computer program from E q s . 4.26 and 4.27.

E = r31.65 - 0.005(Tw)] X lo6 (4.26)

and

CI: = [0.0031(Tw) + 5.911 x lom6 . (4.27)

Although d e t a i l e d stress c a l c u l a t i o n s a r e n o t included i n the SUPEX

computer program, a pre l iminary stress a n a l y s i s of the steam gene ra to r

exchanger was made by hand. This pre l iminary a n a l y s i s was based on t h e

37

W requirements of Sec t ion 111, Nuclear Vessels , of the ASME B o i l e r and

Pressure Vessel Code; and the hand c a l c u l a t e d values a r e compared wi th

allowable va lues i n Table 4.2. The allowable s t ress values were taken

from d a t a i n code case i n t e r p r e t a t i o n s 1315-3 (Ref. 16) and 1331-4

(Ref. 17) .

Table 4.2. Prel iminary Stress Ca lcu la t ions f o r MSBR Steam Generator

Maximum stress i n t e n s i t y , p s i a

Tube Calculated

b A 1 lowab l e

She 11 Ca 1 cu l a t e d

A 1 lowab leL

Pm = 13,900;

P m = 15,500;

(Pm -I- Q) = 30,900

(Pm -I- Q ) = 46,500

pm = 5800;

p m = 8800;

(Pm + Q) = 13,200

(Pm + Q ) = 26,400

Maximum tube s h e e t s t r e s s , p s i Ca 1 cu l a te d

d A 1 lowab le

C17,OOO

17,000

a The symbols a r e those of Sect ion 111 of the ASME B o i l e r and Pressure Vessel Code where

Pm = primary membrane stress i n t e n s i t y , p s i ,

Q = secondary s t r e s s i n t e n s i t y , p s i ,

Sm = allowable stress i n t e n s i t y , p s i .

bBased on a temperature of 1038°F f o r the i n s i d e su r face o f the tubes; t h i s r e p r e s e n t s the worst stress condi t ion.

s a l t of 1150°F.

C Based on the maximum o r h i g h e s t temperature of the coolant

dBased on a temperature of 1000°F f o r the steam and use of a b a f f l e on the s h e l l s i d e .

4 . 3 Descr ipt ion of SUPEX

The equat ions descr ibed i n Subsect ion 4.2 a r e used i n the SUPEX pro-

gram t o s i z e the steam gene ra to r exchanger f o r the s p e c i f i e d inpu t da t a .

A flow diagram of the SUPEX program, a l i s t of the inpu t r equ i r ed , and a

l i s t of the output received from the computer a r e given i n Appendix D.

38

I n the SUPEX program, the t o t a l h e a t t o be t r a n s f e r r e d i n the

exchanger i s d iv ided i n t o a s p e c i f i e d number o f equal increments .

each increment, h e a t ba lance r e l a t i o n s f o r the coolan t s a l t and the

s u p e r c r i t i c a l f l u i d and the h e a t t r a n s f e r equa t ions a r e used t o determine

the change of temperature f o r each s t ream and the tube l eng th r equ i r ed .

The p res su re drop i n the s u p e r c r i t i c a l f l u i d f o r each increment and the

p re s su re drop i n the coolan t s a l t f o r each b a f f l e space a r e c a l u l a t e d

and summed.

For

Two major i t e r a t i o n loops a r e contained i n the SUPEX program.

F i r s t , the b a f f l e spac ing i s assumed and i t e r a t i o n s a r e made u n t i l the

t o t a l c a l c u l a t e d s h e l l - s i d e p re s su re drop agrees wi th t h a t s p e c i f i e d .

I n t e r n a l t o t h i s loop, the number of tubes i n the exchanger i s e s t ima ted ,

and i t e r a t i o n s a r e made t o give the t o t a l tube-side p re s su re drop spec i -

f i e d . A s i m p l i f i e d f low diagram of the SUPEX program, a complete l i s t -

i n g of t he program, and a l i s t of t e r m s used i n the program a r e given i n

Appendix D.

Output from the program inc ludes the number o f tubes , i n s i d e diam-

e t e r of the s h e l l , l ength of t he exchanger, b a f f l e spac ing , number of

b a f f l e s , t o t a l h e a t t r a n s f e r a r e a , and the apparent o v e r a l l h e a t t r a n s f e r

c o e f f i c i e n t . The method of c a l c u l a t i o n used in t h e program permi ts t he

t o t a l l eng th of t he tubes t o d i f f e r from the t o t a l l eng th of t he b a f f l e

space by a f r a c t i o n of the b a f f l e spacing. Both lengths a r e given i n

the ou tpu t , a s a r e the h e a t t r a n s f e r a r ea and apparent h e a t t r a n s f e r

c o e f f i c i e n t f o r each length . The ou tpu t a l s o inc ludes p e r t i n e n t informa-

t i o n f o r each b a f f l e spacing and tube increment.

To i l l u s t r a t e t he use of the SUPEX program, the computer i npu t da t a

f o r the MSBR steam genera tor superhea ter exchanger descr ibed i n Subsec-

t i o n 4.1 and the output d a t a p r i n t e d by the computer a r e included i n

Appendix D.

t h i s program i s about 30 seconds.

The t i m e r equ i r ed f o r a t y p i c a l I B M 360 /91 computer run of

39

4 . 4 Evaluat ion of SUPEX

The problem of s t a b i l i t y i n the steam gene ra to r supe rhea te r was 1 9 considered.

i n s t a b i l i t i e s i n steam gene ra to r s can a r i s e from two sources . F i r s t , a

t r u e thermodynamic i n s t a b i l i t y can e x i s t where, f o r a given p r e s s u r e drop

A s i n d i c a t e d by K. Goldman e t a1.l' and by L. S. Tong,

ac ross the tube, the flow r a t e through the tube may be changed from one

s t e a d y - s t a t e va lue t o another by a f i n i t e d i s tu rbance . Second, a system

i n s t a b i l i t y t h a t i s caused by resonant cond i t ions i n the f l u i d can e x i s t .

Data r e l a t e d t o the f i r s t type of i n s t a b i l i t y have been r epor t ed by L. Y.

Krasyakova and B . N . GluskerY2' and d a t a r e l a t e d t o the second type of

i n s t a b i l i t y have been r epor t ed by E . R. Quandt21 and by L. M. Shotkin.22

A q u a l i t a t i v e e v a l u a t i o n of these d a t a i n d i c a t e s t h a t the mass flow r a t e ,

p re s su re drop, and h e a t f l u x used i n the h o r i z o n t a l U-tube and U-shel l

design w i l l r e s u l t i n s t a b l e ope ra t ion . Operation of a t es t module w i l l

provide f u r t h e r information about the s t a b i l i t y of t h i s design concept.

An a n a l y s i s was made t o e v a l u a t e the v a r i o u s u n c e r t a i n t i e s involved

i n the SUPEX computer program. Tolerances were placed on the phys ica l

p r o p e r t i e s o f the coolant s a l t , the h e a t t r a n s f e r c o e f f i c i e n t s , and on

the pressure-drop c o r r e l a t i o n . The program was run f o r va r ious cases t o

determine the q u a n t i t a t i v e va lues of the favorable and the adverse e f f e c t s

of the u n c e r t a i n t i e s . The favorable e f f e c t s were de f ined a s decreased

h e a t t r a n s f e r a r e a , decreased s h e l l diameter , and decreased t o t a l tube

length. The adverse e f f e c t s were de f ined a s inc reased values f o r t hese

same t h r e e parameters. The s e l e c t i o n of t hese parameters was based on

the b e l i e f t h a t t he h e a t t r a n s f e r a r e a i s i n d i c a t i v e o f the t o t a l c o s t of

the exchanger, the diameter of the s h e l l i s i n d i c a t i v e of the stress prob-

l e m , and the t o t a l l eng th of the tubes i s i n d i c a t i v e of the phys ica l s ize

of the exchanger.

The range of u n c e r t a i n t i e s s t u d i e d included the phys ica l p r o p e r t i e s

of the coo lan t s a l t w i th a d e v i a t i o n of 22% f o r the s p e c i f i c h e a t and

dens i ty and a d e v i a t i o n of 510% f o r t h e v i s c o s i t y and thermal conduc t iv i ty ,

the tube-side and s h e l l - s i d e heat t ransfer c o e f f i c i e n t s w i th a d e v i a t i o n

of - + 20%, and the pressure-drop c o r r e l a t i o n with a d e v i a t i o n of _+lo%.

40

Scru t iny of the s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t r evea led t h a t

p o s i t i v e dev ia t ions ( i n c r e a s e s ) i n the s p e c i f i c h e a t and thermal conduc-

t i v i t y of the coolant s a l t and nega t ive d e v i a t i o n s (dec reases ) i n the

d e n s i t y and v i s c o s i t y of the s a l t w i l l produce f avorab le e f f e c t s , while

oppos i t e d e v i a t i o n s w i l l produce adverse e f f e c t s . A nega t ive dev ia t ion

(decrease) i n the c a l c u l a t e d p res su re drop w i l l produce f avorab le e f f e c t s ,

while a p o s i t i v e d e v i a t i o n ( i n c r e a s e ) w i l l produce adverse e f f e c t s .

The r e s u l t s of t h i s a n a l y s i s i n terms of percentage changes r e l a t i v e

t o the design case a r e given i n Table 4 . 3 . Case 1 i s f o r an inc reased

s p e c i f i c h e a t and d e n s i t y of the coolant s a l t and a decreased v i s c o s i t y

and thermal conduc t iv i ty . Case 2 i s f o r d e v i a t i o n s oppos i t e t o those of

Case 1. Cases 3 and 4 a r e f o r i nc reased and decreased, r e s p e c t i v e l y ,

s h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t s ; Cases 5 and 6 a r e f o r increased

and decreased, r e s p e c t i v e l y , tube-side h e a t t r a n s f e r c o e f f i c i e n t s ; and

Cases 7 and 8 a r e f o r decreased and inc reased , r e s p e c t i v e l y , c a l c u l a t e d

p res su re drops. Case 9 f o r o v e r a l l favorable cond i t ions i s f o r t he com-

bined e f f e c t of a l l favorable changes, and Case 10 f o r o v e r a l l adverse

cond i t ions i s f o r a l l adverse changes. Cases 1, 3 , 5, and 7 r e p r e s e n t

favorable changes; while Cases 2 , 4 , 6 , and 8 r e p r e s e n t adverse changes.

Table 4 . 3 . Percentage Deviations Resul t ing From C a l c u l a t i o n a l U n c e r t a i n t i e s Related t o MSBR Steam Generator Exchanger

Heat To ta l T rans fe r S h e l l Tube

Case Conditions Area Diameter Length

1 2 3 4 5 6 7 8 9

10

Favorable phys i ca l p r o p e r t i e s Adverse phys ica l p r o p e r t i e s Increased s h e l l - s i d e h e a t t r a n s f e r Decreased s h e l l - s i d e h e a t t r a n s f e r Increased tube-side h e a t t r a n s f e r Decreased tube-side h e a t t r a n s f e r Decreased c a l c u l a t e d p res su re drop Increased c a l c u l a t e d p res su re drop Overal l favorable Overal l adverse

-8.2 +7.6

-10.1 +13.5

- 2 . 3 +4 .2 -2.6 +1.8

- 2 1 +3 0

-1.4 +1.2 -1.6 +2.1 -0.5 W.9 -0.5 +0.7 -4 +5

-5.6 +5.2

+8.8

+2.3 -1.6 4-0.5

-7 .0

- 1 . 3

- 15 +18

41

REFERENCES

1. C. G. Lawson, R. J. Kedl, and R. E . McDonald, "Enhanced Heat T rans fe r Tube f o r Hor i zon ta l Condenser With Poss ib l e Applicat ion i n Nuclear _ _ Power P l a n t Design," Transact ions of the American Nuclear Soc ie ty , Vol. 9 , No. 2 (1966).

2. C. G. Lawson, Oak Ridge Nat ional Laboratory, pe r sona l communication

3.

t o C. E . Be t t i s , Oak Ridge Nat ional Laboratory.

H. A. McLain, "Revised Primary S a l t Heat T rans fe r C o e f f i c i e n t f o r MSBR Primary Heat Exchanger Design," ORNL i n t e r n a l correspondence MSR-67-70, J u l y 31, 1969.

4. 0. P. Be rge l in , G. A. Brown, and A. P. Colburn, "Heat T rans fe r and F l u i d F r i c t i o n During Flow Across Bank of Tubes -V: A Study of a C y l i n d r i c a l Ba f f l ed Exchanger Without I n t e r n a l Leakage," Trans. ASME, 76: 841-850 (1954).

5. 0 . P. Berge l in , K. J. Bell , and M. D. Leighton, "Heat T rans fe r and F lu id F r i c t i o n Druing Flow Across Banks of Tubes - V I : The E f f e c t of I n t e r n a l Leakages Within Segmentally Baf f l ed Exchangers," Trans.

6. B. Cox, "Preliminary Heat T rans fe r Resu l t s With a Molten S a l t Mixture

- ASME, 80: 53-60 (1958).

Containing LiF-BeFz-ThF4-UF4 Flowing I n s i d e a Smooth, Horizontal Tube," ORNL i n t e r n a l document CF-69-9-44, September 25, 1969.

7. E . N. S i ede r and G. E. Ta te , "Heat T rans fe r and Pressure Drop o f Liquids i n Tubes," I n d u s t r i a l and Engineering Chemistry, 28 ( i2 ) : 1429- 1435 (1936) *

8. H. W . Hoffman and S. I. Cohen, "Fused S a l t Heat T rans fe r , P a r t 111: Forced Convection Heat T rans fe r i n C i r c u l a r Tubes Containing the S a l t Mixture NaNOz-NaNOs-KN03 , I t USAEC Report ORNL-2433 , Oak Ridge Nat ional Laboratory, March 1960.

H. A. McLain, "Revised C o r r e l a t i o n s f o r the MSBR Primary S a l t Heat T rans fe r C o e f f i c i e n t , " ORNL i n t e r n a l correspondence MSR-69-89 , September 24, 1969.

10. D. A . Donohue, "Heat T rans fe r and Pressure Drop i n Heat Exchangers," I n d u s t r i a l and Engineering Chemistry, 41(11): 2499-2511 (November 1949).

11. J. R. McWherter, "MSBR Mark I Primary and Secondary S a l t s and Their Phys ica l P r o p e r t i e s , " ORNL i n t e r n a l correspondence MSR-68-135, Rev. 1, February 1 2 , 1969.

1 2 . H. S . Swenson, C. R. Kakarala, and J. A. Carver, "Heat T rans fe r t o S u p e r c r i t i c a l Water i n Smooth-Bore Tubes," Transact ions of the ASME, Series C: Jou rna l of Heat T rans fe r , 87(4): 477-484 (November 1965).

John Wiley and Sons, New York, 1936.

9.

13. J . H. Keenan and F. G. Keyes, Thermodynamic P r o p e r t i e s of Steam,

42

14.

1s.

16.

17.

18.

19.

20.

21.

22.

E . S . Nowak and R. J. Grosh, "An I n v e s t i g a t i o n of C e r t a i n Thermodynamic and Transport P r o p e r t i e s of Water and Water Vapor i n the C r i t i c a l Region," USAEC Report ANL-6064, Argonne Nat ional Labora- t o r y , October 1959.

J. F. Harvey, Pressure Vessel Design, D. Van Nostrand Company, New J e r s e y , 1963.

Case 1315-3, "Nickel-Molybdenum-Chromium-Iron Alloy," I n t e r p r e t a - t i o n s of ASME B o i l e r and P res su re Vessel Code, The American Soc ie ty of Mechanical Engineers, New York, A p r i l 25, 1968.

Case 1331-4, "Nuclear Vessels i n High-Temperature S e r v i c e , I' I n t e r p r e - t a t i o n s of ASME B o i l e r and Pressure Vessel Code, The American Soc ie ty of Mechanical Engineers, New York, August 15, 1967.

K. Goldman, S . L. I s r a e l , and D. J . Nolan, "Final S t a t u s Report: Performance Evaluat ion of Heat Exchangers f o r Sodium-Cooled Reactors ,I' Report UNC-5236, United Nuclear Corporation, Elmsford, New York, June 1969.

L. S. Tong, Chapter 7 i n Bo i l ing Heat T rans fe r and Two-Phase Flow, John Wiley and Sons, New York, 1965.

L. Y. Krasyakova and B . N. Glusker, "Hydraulic Study of Three-Pass Panels With Bottom I n l e t Headers f o r Once-Through B o i l e r s , " Teploenerget ika, 12(8): 17-23 (1965), (UDC 532: 621.181.91.001.5).

E. R. Quandt, "Analysis and Measurement of Flow O s c i l l a t i o n s , " Chemical Engineering Progress Symposium S e r i e s , Vol. 57, No. 32, 1961.

L. M. Shotkin, " S t a b i l i t y Considerat ions i n Two-Phase Flow," Nuclear Science and Engineering, 28 : 317-324 (1967).

APPENDICES

45

Appendix A

PHYSICAL PROPERTY DATA

The design p r o p e r t i e s of the f u e l s a l t used i n the concept of a

s i n g l e - f l u i d MSBR and incorporated i n the PRIMEX computer program a r e

given i n Table A . l . The design p r o p e r t i e s of t he coo lan t s a l t used in

t he MSBR concept and inco rpora t ed i n the PRIMEX, RETEX, and SUPEX com-

p u t e r programs a r e given i n Table A.2 ; and the design p r o p e r t i e s of

Has te l loy N used i n the MSBR concept and incorporated i n these computer

programs a r e given i n Table A.3.

Values f o r t he d e n s i t y , v i s c o s i t y , and thermal conduc t iv i ty of the

f u e l and coo lan t s a l t s w e r e taken from d a t a r epor t ed i n Ref. A . l . The

value given f o r the h e a t c a p a c i t y of the f u e l s a l t i s taken from Ref. A

and the value given f o r the h e a t capac i ty of the coolant s a l t i s taken

from Ref. A.3. These r e fe rences a r e l i s t e d below.

A. 1. Oak Ridge Nat ional Laboratory, %Molten-Salt Reactor Program Semi- annual Progress Report August 31, 1969," USAEC Report OWL-4449, February 1970.

annual Progress Report August 31, 1968," USAEC Report ORNL-4344, February 1969.

annual Progress Report February 29, 1969,'' USAEC Report ORNL-4254, August 1969.

A . 2 . Oak Ridge Nat ional Laboratory, "Molten-Salt Reactor Program Semi-

A.3. Oak Ridge Nat ional Laboratory, "Molten-Salt Reactor Program Semi-

46

Table A . 1 . Design P rope r t i e s of MSBR Fuel S a l t

Fuel s a l t components

Composition, mole %

Ap p r ox ima te mo l e cu 1 a r we i gh t

Approximate mel t ing p o i n t , OF

Vapor p re s su re a t 1150"F, mm Hg a Densi ty ,

g/cm3 l b / f t3 A t 1300°F A t 1175 "F A t 1050 OF

b Vi scos i ty , Cent ipoise

l b / f t . h r

A t 1300°F A t 1175°F A t 1050 OF

C He a t cap ac i t y , The rma 1 conduc t i v i t y d

A t 1300 "F A t 1175°F A t 1050 "F

7Li F- BeF2 - ThF, - UF,

71.7-16-12-0.3

64

930

< 0 . 1

p = 3.752 - (6.68 X 10-4)T"C p = 235.0 - 0.02317T"F p = 204.9 l b / f t 3 p = 207.8 l b / f t 3 p = 210.7 l b / f t 3

p = 0.109lexp s] p = 0.2637 exp 7 1 T R p = 17.29 lb/ft-hr p = 23.78 l b / f t * h r p = 34.54 l b / h r . f t

C = 0.324 B tu / lb*"F - -I- 4% P

k = 0.69 B t u / h r * " F . f t k = 0.71 B t u / h r - " F * f t k = 0.69 B t u / h r . " F - f t

~ ~ - ~~~

a

bTable 13.2 on page 145 of Ref A . l .

dFigure 9.13 on page 92 o f Ref. A . l .

F igure 13.6 on page 147 of Ref A . 1 .

Page 163 of Ref. A . 2 . C

The va lue of k shown i s f o r s a l t wi th about 5% less L i F than i n the r e fe rence s a l t . Addi t ion of L i F would inc rease the average va lue t o about 0.72 t o 0.74. The e s t a b l i s h e d and conserva t ive va lue of 0.71 was used i n the c a l c u l a t i o n s f o r the MSBR concept.

47

V Table A.2. Design P rope r t i e s of MSBR Coolant S a l t

Coolant s a l t components

Composition, mole %

Approximate mole cu 1 a r we i gh t

Approximate mel t ing p o i n t , O F

Vapor p re s su re a t 1150°F, mm Hg

Density , g / cm3 l b / f t3 A t 1150°F A t 1000 OF A t 850 "F

b

a

V i scos i ty , Cent ipoise

l b / f t . h r

A t 1150 OF A t 1000 OF A t 850°F

Heat capac i ty

Thermal conduc t iv i ty ,

C

d

A t 1150 "F A t 1000 OF A t 850 OF

NaBF4-NaF

92-8

104

7 25

25 2

p = 2 . 2 5 2 - ( 7 . 1 1 X lO-")T"C p = 141.4 - 0.0247T"F p = 113.0 l b / f t 3 p = 116.7 l b / f t 3 p = 120.4 l b / f t 3

p = 0.0877(exp e) 1-1 = 2.60 l b / f t . h r p = 3.36 l b / f t . h r p = 4.61 l b / f t . h r

C = 0.360 Btu/ lb ."F - -I- 2% P

k = 0.23 Btu /hr . "F . f t k = 0.23 Btu /hr . "F . f t k = 0.26 B t u / h r - " F . f t

a

bTable 13.2 on page 145 of Ref. A . l .

dFigure 9.13 on page 92 of Ref. A . l .

F igure 13.6 on page 147 of Ref. A . l .

Page 168 of Ref. A.3. C

48

Table A.3. Design P rope r t i e s of Has te l loy N

Composition, w t % Nicke 1 Molybdenum Chromium I r o n Manganese S i l i c o n , maximum Boron, maximum Titanium Hafnium o r niobium Cu, Coy P, S , C y W , A 1

Densi ty , l b / f t 3 A t 80°F A t 1300°F

Thermal conduc t iv i ty , B t u / h r * f t . O F

A t 80°F A t 1300 "F

S p e c i f i c h e a t , B tu / lb - O F

A t 80°F A t 1300 "F

Thermal expansion per "F A t 80°F A t 1300 OF

Modulus of e l a s t i c i t y , p s i A t 80°F A t 1300 OF

Tens i l e s t r e n g t h , p s i A t 80°F A t 1300°F

Maximum al lowable des ign stress a t 1300"F, p s i

A t 80°F A t 1300 "F

Balance 1 2 7 0 t o 4 0.2 t o 0.5 0 . 1 0.001 0.5 t o 1.0 0 t o 2 0.35

55 7 54 1

6.0 12.6

0.098 0.136

5.7 x l o+ 9.5 x

31 x lo6 25 X lo6

-1 15 , 000 -75,000

25 , 000 3500

2500 Melt ing temperature , "F

Y

49

Appendix B

THE PRIMEX PROGRAM

The PRIMEX computer program i s o u t l i n e d i n block-diagram form i n

Fig. B . l . The i n p u t d a t a r equ i r ed f o r the program a r e given i n Table

B . l , and the ou tpu t received from the program a r e given i n Table B . 2 .

A complete l i s t i n g of t he main program and i t s two subrou t ines i s f o l -

lowed by d e f i n i t i o n s of the in t e rmed ia t e v a r i a b l e s used i n the program.

To i l l u s t r a t e the use of t he PRIMEX program, the i n p u t and ou tpu t f o r

the MSBR primary h e a t exchanger discussed i n Subsection 2 . 1 of t h i s

r e p o r t a r e p re sen ted a s p r i n t e d by the computer.

50

R E A 0 AN0 P R I N T INPUT DATA

ASSUME B A F F L E SPAC I NG

-.IL b4 ASSUME SHELL

0 I AMETER

CALCULATE NUMBER OF TUBES, FUEL AND COOLANT FLOWS AN0 VAR I OUS GEOMETR I ES

ASSUME EXPANS I ON RAD I US REQU I REO FOR ACCEPTABLE STRESSES

START WITH F I R S T INCREMENT FROM HOT S I D E OF HEAT EXCHANGER 1=1

ASSUME TEMPERATURE OROP FOR THE INCREMENT

EVALUATE ALL P H Y S I C A L PROPERTIES AT AVERAGE TFMPERATURE OF INCREMENT

CALCULATE PRESSURE DROPS AND HEAT TRANSFER

CORRELAT I ON FOR 0 I FFERENT REG I MES COEFF I C I ENTS FOR THE INCREMENT, US I NG CORRECT

CALCULATE HEAT RATE AN0 TEMPERATURE DROPS OF THE INCREMENT

Fig. B.l. Simplified Flow Diagram of the PRIMEX Computer Program. Y

51

TEMPERATURE OROPS AGREE W I T H OUR ASSUMPTION

No CHANGE ASSUMED INCREMENT TEMPERATURE

DROP

- GO TO NEXT INCREMENT I = I + l EN0 TEMPERATURE OF

5 2

- CHANGE ASSUMED BAFFLE SPACING

DOES TOTAL SHELL S I D E PRESSURE DROP

V

.

53

Table B . I . Computer Input Data f o r PRIMEX Program

Card Columns Format va r i a b 1 e T e r m Un i t s

A 1- 10 11-20

B

C

2 1- 30

31-40 41-50

1- 10 11-20 2 1- 30 31-40

1- 10

11-20

2 1- 30 31-40

41-45

h,&. 1-10

DICNPT 11-20 E 1- 10

11-20

2 1- 30

31-35 36-40

41-45

Fl,F2. 1-10 ... 11-20 2 1- 30 31-40 41-50 51-60

E10.4 F10 .O

F10 .O

F10 .O F10 .O

F10 .O F10 .O F1O.O F10 .O

F10 .O

F10 .O

F10.0 F10 .O

I5

F10 .O

F10 .O

F10 .O

F10 .O

F10 .O

I 5 I5

I 5

F10 .O F10 .O F10 .O F10 .O F10 .O F10 .O

Heat load r equ i r ed A 1 lowab 1 e tub e- s i d e p r e s - Allowable s h e l l - s i d e

Tube-side i n l e t p r e s s u r e S h e l l - s i d e o u t l e t p r e s s u r e

Coolant o u t l e t temperature Fuel i n l e t temperature Fuel o u t l e t temperature Coo 1 a n t i n 1 e t t emp e r a t u r e

Leakage f a c t o r f o r h e a t t r a n s f e r c o r r e l a t i o n s

Leakage f a c t o r f o r pres- s u r e drop c a l c u l a t i o n s

Tube material conduc t iv i ty Arc1 o f bent t ube f o r t he r -

mal expansion Number of p a i r p o i n t s i n

S t r e s s i n t e n s i t y t a b l e f o r t ube m a t e r i a l

s u r e drop

p r e s s u r e drop

S t r e s s i n t e n s i t y a t CTM

Temp era t u r e

Radius o f coo lan t c e n t r a l downcomer

Distance between s h e l l w a l l and tube bundle

Maximum a n t i c i p a t e d heat exchanger r a d i u s

Number of cases t o be run Index one i f enhanced

Index one i f s t ress ana l -

temperature

tubes a re used

y s i s i s included

Outside diameter o f t ubes Tube w a l l t h i ckness Radial p i t c h C i rcumfe ren t i a l p i t c h I n n e r b a f f l e c u t Outer b a f f l e c u t

HEATL PRDT

PRDS

TPIN SPOUT

CTO FTO ETF E TC

LK

PLK

WCOND ARC

ICNPT

CASM

CTM

RA5

DTR

RASMAX

KASES KENTB

KTBST

D I A WTHK RPI BCPI CUT3 CUT4

Btu/hr l b / f t 2

lb/ft?

l b / f t 2 l b / f i?

OF OF OF OF

B t u / h r * f t *OF Degrees

p s i

O F

f t

f t

f t

f t f t f t f t % o f a r e a % o f a r e a

54

Table B.2 . Output Data From PRIMEX Computer Program

Term Variab 1 e U n i t s

THEATO

HTPERC

QC

QF

TTDSO

SPPERC

TTDTU

TPPERC

RA8

B S O I

VOL

AREA

SNT

TUBLEN

HEXLEN

STRLEN

EXPRAD

BRL1

PSTO

PQSTO

PQFSTO

PSTI

PQSTI

PQFSTI

SAVT

TAVT

T o t a l h e a t a c t u a l l y t r a n s f e r r e d

Percentage of r equ i r ed h e a t load a c t u a l l y

Coolant ( s h e l l - s i d e ) mass flow r a t e

Fuel ( tube-side) mass flow r a t e

T o t a l t ube - s ide p r e s s u r e drop

Percentage o f allowed tube p r e s s u r e drop

T o t a l s h e l l - s i d e p r e s s u r e drop

Percentage o f allowed s h e l l p r e s s u r e drop

Radius o f hea t exchanger s h e l l

D i s t a n c e between baffles

Flu id volume contained i n tubes

To ta l h e a t t r a n s f e r a r e a i n h e a t exchanger

T o t a l number of tubes

Actual t ube l eng th

Heat exchanger l eng th from lower tube s h e e t

S t r a i g h t s e c t i o n l eng th o f tubes

Radius of t ube bends f o r thermal expansion

Modif icat ion f a c t o r f o r B e r g e l i n ' s h e a t

Primary s t r e s s e s on o u t e r s u r f a c e of tubes

Combined primary and secondary s t resses on

Combined primary, secondary, and peak s t resses on o u t e r s u r f a c e of t ubes

Primary s t resses on i n n e r s u r f a c e o f tubes

Combined primary and secondary s t resses on

Combined primary, secondary, and peak s t resses on inne r s u r f a c e of t ubes

S h e l l average temperature

Tube average temperature

t r a n s f e r r e d

a c t u a l l y used


t o upper nozz le o f t ubes

t r a n s f e r c o r r e l a t i o n

o u t e r s u r f a c e o f tubes

i n n e r s u r f a c e of tubes

Btu/hr

l b / h r

l b /h r

p s i

p s i

f t

f t

f P

fi?

f t

f t

f t

f t

p s i

p s i

p s i

p s i

p s i

p s i

O F

O F Y

W

55

Table B.2 (cont inued)

Term Var i ab le Un i t s

T C I ( I )

TCO( I)

CWT ( I )

TFI (I)

TFO ( I )

FWT(I)

TwJlT (1)

vM1(I)

vM2(I)

v ~ 3 ( 1 )

VWOl ( I )

W03 (I)

PDSO( I)

PDTO ( I)

WNTO ( I)

PRNTO ( I)

RENSOl (I)

ENS02 ( I )

ENS03 (I)

HTO ( I)

AHSO ( I)

UOA ( I )

HEAT (I)

Coolant o u t l e t temperature from increment I

Coolant i n l e t temperature from increment I

Average tube wa l l temperature a t coolan t s i d e

Fuel o u t l e t temperature from increment I

Fuel i n l e t temperature from increment I

Average tube w a l l temperature a t f u e l s i d e

Average temperature drop a c r o s s tube w a l l i n

F lu id average v e l o c i t y i n o u t e r window i n

F lu id average v e l o c i t y i n over lapping b a f f l e zone i n increment I

Flu id average v e l o c i t y i n i n n e r window i n

F lu id v e l o c i t y a c r o s s tubes i n o u t e r edge o f

F lu id v e l o c i t y a c r o s s tubes i n inne r edge of

S h e l l - s i d e p re s su re drop f o r increment I

Tube-side p r e s s u r e drop f o r increment I

Tube-side Reynolds number f o r increment I

Tube-side P rand t l number f o r increment I

Reynolds number i n o u t e r window increment I

Reynolds number i n over lapping b a f f l e zone i n

Reynolds number i n inner window i n

Tube-side hea t t r a n s f e r c o e f f i c i e n t i n

i n c r emen t I

increment I

increment I

b a f f l e i n increment I


increment I

inc renen t I

increment I

S h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t i n increment I

Overall h e a t t r a n s f e r c o e f f i c i e n t i n increment I

Heat t r a n s f e r r e d i n increment I

OF

OF

OF

OF

OF

OF

OF

f t / s e c

f t / s e c

f t / s e c

f t / s e c

f t / s e c

l b / f t 2

l b / f t 2

Btu /hr*f? *OF

Btu/hr*fr? *OF

Btu/hr* f$ #OF

Btu/hr

The PRIMEX Program L i s t i n g

* * F T N T L t E T GTM. PROGRAM MSBRPE-2 T Y P E R E A L LK 9 L A W O l T L A N 0 3 DIMENS I O N TFO( 7 5 1 T T C I ( 7 5 ) TVML ( 7 5 ) T V M ~ ( 7 5 ) T V k C l ( 7 5 ) T V W C 3 ( 7 5 ) T

l R E N T O ( 7 5 ) , P R N T O ( ~ ~ ) T R E N S O ~ ( ~ ~ ) T R E N S O ~ ( ~ ~ ) t R E h S O 3 ( 7 5 ) T

2 V M 3 ( 7 5 ) ~ PDSO ( 7 5 ) T N T ( 1 0 0 1 f B J ( 3 1 T H S O ~ ( 7 5 ) T H S C ~ ( ? ~ ) T H S O ~ ( 7 5 1 T

3AHSO( 7 5 ) tHTO ( 7 5 1 t U O A l 7 5 ) 9TCO ( 7 5 ) T T F I ( 7 5 J r H E A T ( 7 5 T T W D T ( 7 5 I T

4 P D T 0 ( 7 5 ) , T U B L N ( 7 5 1 , 7 5 ) T v 2 ( 7 5 ) T v 3 ( 7 5 ) T V W l ( 7 5 ) T V W 3 ( 7 5 ) T

5 6 C H T ( ~ ~ ) T F W T ( 7 5 j r A V W T ( 7 5 )

R ( 100 ) 9 FACT( 100 1 t TCP I ( 100 J T TOTAL (100 1 tCASM( 6 ) T CTM ( 6

1001 FORMAT( E 1 0 0 4 1 4F10.0) 1 O C 2 FORMAT ( 4F 10 -0 1 1003 FORMAT( ~ F L O O O T I ~ ~ 100 4 FORMAT ( 2 F 10 4 1 1005 FORMAT( 3 F l O o O T 3 1 5 ) 1006 FORMAT( 6F 10.0 1 1007 FORMAT ( ~ H ~ T ~ X T ~ H I T ~ X T ~ H C T M ~ ~ X ~ ~ H C A S M / / ( ~ X ~ I ~ ~ ~ F ~ Z . ~ ) ) 1 0 0 8 FORMAT(22HOHEAT LOAD REQUIRED = T F ~ ~ . O T ~ X T ~ H ( B T U / H R I 1 1009 FORMAT(43HOALLOWABLE TOTAL TUBE-S IDE PRESSURE DRCP = r F l O o O v 2 X t

1 l O H ( L B / S Q - F T ) 1

1 l O H ( L B / S Q - F T ) 1 1010 FORMAT(44HCALLOWABLE T C T A L S H E L L - S I D E PRESSURE CROP = r F 1 0 . O t 2 X t

1011 FORMAT(23HOTUBE I N L E T PRESSURE = T F ~ O . O T ~ X T ~ C H ( LB/SQ-FTJ 1 1012 FORMAT ( 2 4 H O S H E L L OUTLET PRESSURE =t F ~ O ~ O T Z X T 1OH ( L B I S Q - F T ) I 1013 F O R M A T ( 3 3 H O H I G H TEMP. OF SHELL S I D E F L U I D = T F ~ O . ~ T ~ X T ~ H ( F ) ) 1014 F O R M A T ( 3 3 H O H I G H TEMP. OF TUBE S I O E F L U I D = T F ~ O * Z T Z X T ~ H ( F ) J 1 0 1 5 FORMAT(32HOLOW TEMP, OF TUBE S I D E F L U I D = T F ~ O . ~ T ~ X T ~ H ( F I ) 1016 FORMAT(32HOLOW TEMP. OF SHELL S I O E F L U I D = T F ~ C ! . Z T Z X T ~ H ( F I ) 1017 FORMAT( 32HOHEAT TRANSFER LEAKAGE FACTOR = TF10.5) 1 0 1 8 FORMAT(27HOPRESSURE LEAKAGE FACTCR = t F l O . 5 1 1019 FORMAT(35HOCONOUCTIVETY OF TUBE kALL METAL = r F L @ . S ~ 2 x 9

1 1 3 H ( BTU/HR-FT-F) 1

MSBRP 10 MSBRP 20 MSBRP 30 MSBRP 3 1 MSBRP 3 2 MSBRP 33 MSBRP 34 MSBRP 35 MSBRP 36 MSBRP 40 MSBRP 50 MSBRP 60 MSBRP 70 cn MSBRP 80 rn MSBRP 90 MSBR 100 MSBR 110 MSBR 1 2 0 MSBR 1 2 1 MSBR 130 MSBR 131 MSBR 140 MSBR 150 MSBR 160 MSBR 170 MSBR 1 8 0 MSBR 190 MSBR 200 MSBR 210 MSBR 220 MSBR 221

1C20 FORMAT(37HOARC OF FOUR BENDS FOR F L E X I B I L I T Y = r F 1 0 0 2 r 2 X r MSBR 2 3 0 1 9 H ( D E G R E E S ) ) MSBR 231

1022 FORMAT(41HODISTANCE BETkEEN SHELL WALL AND TUBES = MSBR 250 1 r F l O o 5 r 2 X r 6 H ( F E E T ) ) MSBR 2 5 1

1 0 2 3 FORMAT(4SHOMAXIMUM A N T I C I P A T E D OUTER R A D I U S CF EXCHANGER = 9 MSBR 260 1 F 1 0 * 5 r 2 X r 6 H ( F E E T ) 1 MSBR 261

1024 FORMAT(23HONLMBER OF CASES RUN = 114) MSBR 270

1s ARE U S E D ) ) MSBR 2 8 1 1026 FORMAT( l I ’Or36HUSE OF STRESS A N A L Y S I S S U B R C U T I h E = 9 MSBR 290

1 I 4 , 2 X r 1 9 H ( O N E I F TO BE U S E D ) ) MSBR 291 1027 FORMAT(29HOOUTSIDE DIAMETER OF TUBES = r F l O o 5 9 2 X r 6 H ( F E E T ) ) MSBR 300 1028 FORMAT(27HOWALL THICKNESS OF TUBES = r F l O o 5 r 2 X r 6 H ( F E E T ) ) MSBR 310 1029 F O R M A T ( 1 6 H O R A D I A L P I T C H = r F l O o 5 r 2 X r 6 H ( F E E T ) ) MSBR 320 1 0 3 0 FORMAT(25HOCIRCUMFERENTIAL P I T C H = 9 F 1 0 e 5 r 2 X r 6 H ( F E E T ) 1 MSBR 330 1031 FORMAT422HOINNER BAFFLE C U T 3 = r F L O o 5 , 2 X v 1 0 H ( P E R CEhTJ ) MSBR 340

1033 F O R M A T ( 2 5 H l T O T A L HEAT TRANSFERED = 9F12.0 r 2 X r 8 H ( B T U / H R ) 9 MSBR 360 1 2 x 9 1H( r F 5 o l r 9 H PERCENT) ) MSBR 361

1034 FORMAT(29HOMASS FLOW RATE OF COOLANT = , F l O o O r 2 X , 7 H ( L B / H R ) MSBR 370 1 0 3 5 FORMPT(26HOMASS FLOW RATE OF F U E L = r F 1 0 0 O r 2 X 1 7 H ( L B / H R ) 1 MSBR 380

1 r 2 X q l H ( , F 5 o l r 9 H P E R C E N T ) ) MSBR 391

1 2 X r l H ( r F 5 o l r 9 H PERCENT) MSBR 401 1 0 3 8 FORMAT( 24HONOMINAL SHELL R A D I U S = r F 7 . 4 , 2 X r 4 H ( F T ) 1 MSBR 410 1039 FORMAT(26HOUNIFORM BAFFLE S P A C I N G = , F 7 o 4 r Z X 1 4 H ( F T ) I MSBR 420 1040 FORMAT(40HOTUBE F L U I D VOLUME CONTAINED I N TUBES = r F 7 0 2 1 1 X 9 MSBR 430

l l Z H ( C U B 1 C F E E T ) ) MSBR 431 1041 F O R M A T ( l P 0 ~ 4 6 H T O T A L HEAT TRANSFER AREA BASED ON TUBE COD. = t MSBR 440

1 F 1 2 * 2 r 2 X 1 6 H ( S Q F T ) ) MSBR 441 1 0 4 2 FORMAT(25HOTOTAL NUMBER OF T L B E S = r F O . 0 1 MSBR 4 5 0 1043 FORMAT(21HOTOTAL TUBE LENGTH = r F 6 . 2 , 2 X r 4 H ( F T ) 1 MSBR 4 6 C 1044 FORMAT(29HOHEAT EXCH. APPROXe LENGTH = r F 6 o Z r 2 X 1 6 H ( F E E T I I MSBR 470 1045 FORMAT(35HOSTRAIGHT S E C T I G N OF TUBE LENGTH = r F 6 * 2 r 2 X 1 4 H ( F T ) 1 MSBR 480

1021 F O R M A T ( 3 4 H O I N S I D E R A D I U S OF OUTER ANNULUS = r F l O o 5 r 2 X r 6 H ( F E E T ) 1 MSBR 240

1025 FORMAT(25HOUSE OF ENHANCED TUBES = , 1 4 r 2 X r 3 2 H ( O N E I F ENHANCED TUBEMSBR 2 8 0

1032 FORMAT(22HOOUTER BAFFLE C U T 4 = r F l O o 5 r 2 X r 1 0 H t P E R C E A T ) MSBR 350 cn U

1036 FORMAT(34HOSHELL-S IDE TOTAL PRESSURE DROP = r F 1 0 . 2 9 2 X 1 9 H ( L B / S Q I N ) M S B R 390

1037 FORMAT(33HOTUBE-S IDE T C T A L PRESSURE DROP = r F l O o 2 r 2 X I 9 H ( L B / S Q I N ) r M S B R 400

1046 FORMAT(38HORADIUS G F THERMAL E X P A N S I O N CURVES = r F 6 0 2 r 2 X 1 6 H ( f E E T ) IMSBR 490

1047 F O R M A T ( 3 1 H O B E R G L I h M O D I F I C A T I O N FACTOR = r F 5 . 2 ) 1 0 4 8 FORMAT ( l H 0 1 2 X r 1 H I 9 7 x 9 3 H T C I r 9 X t 3 H T C O r 9 X 9 3 H C k T r 9 X 9

19x1 3 F F W T r 8 X r 4 H T W D T / / l l X r 1HF r l l X r l H F 9 1 l X r l H F ~ l l X r 2

3 H T F I r 9 X 9 3 H T F O t

l k F , 11x1 1 H F r 1 1 X t l H F 9 1 1 X r l H F / / 4 1 X t I 3 r 7 E 1 E * 4 1 ) 1049 FORMAT( l H 0 , 2 X , l H I 1 9 X r 2 H V l 9 9 X r 2 H V 2 v 9 X r 2 H V 3 r 9 X r 3 H V W l t 9 X r 3 H V W 3 r

1 8 X ~ 4 H P D S 0 ~ 8 X r 4 H P D T O / / 3 2 X 1 6 H F T / S E C 1 3 3 X ~ 7 H L B / S Q F l / / ~ l X t I 3 r 7 F l 2 ~ 4 ~ ) FORMAT( l H O r 2 X 9 l H I r 5 X r 5 H R E N T O r 7 X t 5HPRNTO r 7 X ~ 6 H P E h S C l r 6 X r 6 H R E N S 0 2 r 1 0 5 0

16x9 6HREN SO39 7 X , 3HHTOr 8X r 4 H A H SO 9 9 X r3HUOA 18 X p 4 H H E A T / / 7 7 X r 2 1 3 H B T U / H R / S Q F T / F r l 3 X , 6 H B T U / H R / / ( l X r I 3 r 9 E L 2 . 4 ) 1

1 0 5 1 F O R M A T ( 2 7 H O T U B E WALL AVERAGE TEMP. = r F 1 0 . 2 ) 1 0 5 2 F O R M A T ( 2 8 H O S H E L L S I D E AVERAGE TEMP. = T F10.2) 1 0 5 3 F O R M A T ( l H O q 3 4 H P STRESS A T TUBE OD AND TUBE ID = 2 F 1 0 * 2 r l X r

1 9 H ( L B / S Q I N ) / / 1 8 H ( SHOULD NOT E X C E E D r F l O o 2 r 3 H I I 1 0 5 4 F O R M A T ( l H O r 3 6 H P + Q STRESS AT TUBE OD AND TUBE I D = 9

1 2F10 .2 , lX,9H(LB/SQIN)//18H(SHOULD NGT EXCEEDIFLO. 29 2 3 H 1 )

1055 F O R M A T ( l P 0 , 3 8 H P + Q + F STRESS AT TUBE OD AND TUBE I D = 9

1 2 F 1 0 , 2 9 1 X 9 9 H ( L B / S Q I N I / / 1 8 H ( SHOULD NGT EXCEED, F l O 2 9

2 3 H 1 ) C C R E A D I N AND P R I N T OUT I N P U T DATA

K E Y 7 = 1 V M l ( l ) = O * VM2( 1)=0* V M 3 ( 1)=0. V W O l t 1 1 5 0 . V W 0 3 ( l ) = C . R E N S O l t 1 I=O. R E N S 0 2 ( 1 ) = O * R E N S 0 3 ( 1 )=O* H S O 1 ( 1 )=O. H S 0 2 ( 1)=0. H S 0 3 ( 1 j =0. H E F I = 1. HEFO = 1.

C

MS BR MSBR MS BR MSBR MSBR MSBR MS BR MSBR MS BR MS BR MSBR MSBR

500 5 10 5 11 5 12 5 20 5 2 1 5 3 0 5 3 1 532 5 40 5 50 5 6C

MSBR 561 MSBR 570 MSBR 571 MSBR 5 7 2 MSBR 580 MSBR 5 8 1 MSBR 582 MSBR 650 MSBR 660 MSBR 610 MSBR 620 MSBR 630 MSBR 640 MSBR 650 MSBR 660 MSBR 670 MSBR 6 8 0 MSBR 690 MSBR 700 MSBR 710 MSBR 720 MSBR 730 MSBR 740 MSBR 810

READ 1001, HEATL, PRDT, PROS t T P 1 N v S P O U T READ 1 0 0 2 1 CTOI FTOI ETF, ETC READ 1003, LK, PLK, WCONDvARC , I C N P T R E A D 10049 ( C A S M ( K ) r C T M ( K ) r K = l * I C N P T l READ 1 0 0 5 9 RA5, DTRI R A ~ M A X I K A S E S I K E N T B I K T B S T

R E A D 1006, D I A , WTHKI R P I , B C P I , CUT39 CUT4 H S F C T = l . I F ( FTO.LT.CT0) HSFCTZ-1. P R I N T 1007 P R I N T 1008, HEATL P R I N T 1C091 PRDT P R I N T 1Cl0, PROS P R I N T 1011, T P I N P R I N T 1 0 1 2 , SPOUT P R I N T 1013, CTO P R I N T 1014, FTO P R I N T 10159 ETF P R I N T 1016, ETC P R I N T 10179 LK P R I N T 1018, PLK P R I N T 10 19, WCOND P R I N T 10209 ARC P R I N T 1 0 2 1 , R A 5 P R I N T 1 0 2 2 9 DTR P R I N T 1023, RA8MAX P R I N T 1 0 2 4 t KASES P R I N T 1025, KENTB P R I N T 1 0 2 6 , K T B S T P R I N T 1 0 2 7 9 D I A P R I N T 1028, WTHK P R I N T 1 0 2 9 , R P I P R I N T 1030, B C P I P R I N T 1031, CUT3 P R I N T 10132, CUT4

1 CONTINUE

( Kc CTM( K 1 ,CA SM ( K ) t K = l t I C N P T )

C

MSBR 760 MSBR 770 MSBR 780 MSBR 790 MSBR 8 0 0 MSBR 810 MSBR 820

MSBR 830 MSBR 840 MSBR 850 MSBR 860 MSBR 870 MSBR 880 MSBR 890 MSBR 900 MSBR 910 MSBR 9 2 0 MSBR 930 MSBR 940 MSBR 9 5 0 MSBR 960 MSBR 970 MSBR 9 8 0 MSBR 990 MSB l O C 0 MSB 1010 MSB 1 0 2 0 MSB 1@3@ MSB 1040 MSB 1050 MSB 1060 MSB 1C70 MSB 1080 MSB 1650

C B E G I N GEGMETRY C A L C U L A T I O N S FOR S I N G L E ANNULLS CCUNTER FLOW C D I S C AND DOUGHNUT B A F F L E D H E A T EXCHANGER

ARCR= @.017452*ARC ATUBE = (3.141598 ( D I A * * 2 . 0 ) ) / 4 . 0 G F T T = 1*/36C'r). GFT = 1./144. D I A I = D I A - 2 * 0 * W T H K F A T U B = ( 3 0 1 4 1 5 9 * ( D I A I * * 2 . 0 ) I / 4 . C K E Y 1 = 0 P E R C l = 0.99

K E Y 2 = 0

R A 8 L = R A 5 R A8H=RA8 MAX

2 I F ( KEY 1. GT .C ) B SO I=O 54( BSL+B SH)

P E R C 2 = (2.99

3 R A 8 = 0 * 5 * ( R A 8 L +RA8H I R J 8 = ( R A 8 - R A 5 - 2 . * D T R l / R P I + l o I J 8 = R J 8 R I J 8 = I J 8 I F ( R J 8-R I J 8-0 5 1 4 9 4 9 5

4 J 8 = i J 8 T RP I = ( RA 8-R A 5- 2 *D TR 1 / 4 R I J 8- 1 l C P I = B C P I * R P I / T R P I GO TO 6

5 J 8=I J 8 + 1 T RP I = ( R A 8-R A 5- 2 *D TR I /R I J 8 C P I = B C P I * R P I / T R P I

R ( I 1 =RA5+DTR +TRP I* ( I - 1 1 6 DO 7 I = l * J 8

F A C T ( I I = 6 0 2 8 3 1 8 * R ( I 1 N T ( I ) = F A C T ( I I / C P I TCP I ( I )=FACT ( I I / N T ( I ) I F ( I . E Q * l ) T O T A L ( I 1 = N T ( I I I F ( I .NE 1) TOTAL ( I I =TOTAL ( 1-1 1 +NT ( 1 1 7 NTO=TOTAC( J 8 I SNT=NTO R A 5 2 = R A 5 * * 2 R A 8 2 = R A 8 * * 2

MSB 1660 MSB 1670 MSB 1120 MSB 1130 MSB 1140 MSB 1150 MSB 1160 MSB 1170 MSB 1180 MSB 1190 MSB 1200 MSB 1210 MSB 1220 MSB 1230 MSB 1240 MSB 1250 MSB 1260 MSB 1270 MSB 1280 MSB 1290 MSB 1300 MSB 1310 MSB 1320 MSB 1330 MSB 1340 MSB 1350 MSB 1360 MSB 1370 MSB 1380 MSB 1390 MSB 1400 MSB 1410 MSB 1420 MSB 1430 MSB 1440 MSB 1450 MSB 146@ MSB 1470

0

R A 6 = ( RA52+CUT4* ( RA 8 2 - R A 5 2 1 1 **. 5 J 6 = ( R A 6 - R ( 1) ) / T R P I + l ,

R A 7 = ( RA82-CUT3*( RA 82-RA 52 1 I * * . 5 J 7 = ( R A 7 - R ( 1) ) / T R P I + l .

RA62=RA6**2 RA72=RA7**2

R B 2 = J 7 - J 6

SUM l = T O T A L ( J 8 -TOTAL ( J 7 j SUM2=TOTAL ( J 7 1 -TOTAL ( J 6 ) SUM 3=TOT AL ( J 0 1 I S U M l = S U M l I SUM2=SUM2 ISUM3=SUM3

RA6=R( J6 I + . 5*TRP I

RA7=R ( J 7 I + 5*TRP I

R B 1 =O 5* ( J 8- J 7

R B3=0 5* J6

BSM AX= 1 5* ( ( RA 8- ( R A 8-RA 7 1 /2 I - ( R A 5+ ( RA6-RA5 1 42 1 1 BSM IN=O. 2s ( R P8-RA5 1 I F ( B S M I N o L T . O o 1 6 6 7 ) B S M I N = 0 . 1 6 6 7 AP01=3 .14159* (RA82-RA72 ) -ATUBE*SUMl AP03=3. 14159W RA62-RA52 )-ATUBE*SUM3 LAWO1=6.28318*RA7- 5 * D I A * ( N T ( J 7 I +NT( J7+1) 1 LAW03=6 .28318*RA6- .5 *D IA* (NT( J 6 ) + N T ( J6+1) 1 HW=2.*WCOND/(DIA*(ALOG( D I A / D I A I 1 4 1 CSPHAV=0.36 FSPHAV=0.324 QC=HEATL/ (CSPHAV*(CTO-ETC I ) QF=HEATL/( FSPHAV*( FTO-ETF) GTO = QF/( NTO*FATUB 1 K E Y 3=0

XPRMIN= 0. X P RM AX= 6 0

8 EXPRADz 0.5* ( X P R M I N+XPRMAX) IF( KTBST.EQ.0) EXPRAD=l . 77 I F( K EY 1 . EQ .O I B SH=B S M A X I F ( K E Y 1. EQ.O)BSL=BSMIN

MSB 1480 MSB 1490 MSB 1500 MSB 1510 MSB 1520 MSB 1530 MSB 1540 MSB 1550 MSB 1560 MSB 1570 MSB 1580 MSB 1590 MSB 1600 MSB 1610 MSB 1620 MSB 1630 MSB 1640

MSB 1660 MSB 1670 MSB 1680 MSB 1690 MSB 1700 MSB 1710 MSB 1720 MSB 1730 MSB 1740 MSB 1750 MSB 1760 MSB 1770 MSB 1780 MSB 1790 MSB 1800 MSB 1810 MSB 1820 M S 0 1830 MSB 1840

MSB 1650 m +

IF(KEYl.EQ.O~BSOI=O.59(8SL+BSH) CURV ES=0 .O 69 813*ARC* EXPRAD+ 0.4*(RA8-RA51+.25*BSOI IT = 0 KFINAL=O

9 I=1 TSUM=O. SSUM=O. THEATO = 0.0 TPDTO = 0.0 TPDSO = 0.0 TFO( I )=FTO TCI(II=CTO TIF=-5.0 TIC=-5.0 CDTF=O. FDTF=O. BSO = BSOI BRL 1 = BSO/((RA8-(RA8-RA7)/2.)-(RA5+(RAb-RA5)/2.J) GBRL = 0.77*BRLl**(-,138) AWO 1 = BSO*LAWOl AW03 = BSO*LAW03 AWL = SQRT(AWOl*APOl1 AW2 = (AWOl+AW03)/2. AW3 = SQRT( AW03*AP03) GSOl = QC/AWl GS02 = QC/AW2 GS03 = QC/AW3 BSO=CURV ES EQVBSO= CURVES+ 13.*iDIA+DIAI 1 KEY4=0

10 KEY5=0 11 ATC = TCI(1) + (TIC/2.0)

CFT = ATC +.CDTF*HSFCT ATF = TFO(I)+TIF/2. FFT=ATF-FOTF*HSFCT FI=I TUBLN(1) =(FI-1. j*BSOI+CURVES CVIS=0.2121*EXP(4C32./(460.+ATC)I

MSB 1850 MSB 1860 MSB 1870 MSB 1880 MSB 1890 MSB 1900 MSB 1910 MS8 1920 MSB 1930 MSB 1940 MSB 1950 MSB 1960 MSB 1970 MSB 1980 MSB 199C MSB 2000 MSB 2010 MSB 2020 m MSB 2030

N

MSB 2040 MS8 2050 MSB 2060 MS8 2070 MSB 2C80 MSB 2090 MS8 2100 MSB 2110 MSB 2120 MSB 2130 MSB 2140 MSB 2150 MSB 2160

MSB 2180

MSB 22C0 MSB 2210 MSB 2220

( I 1 (

CV I SW=O 2121*EXP ( 4 0 3 2 . / (460. +CFT 1 1 MSB 2230 CDEN=141 .37 -0 .02466*ATC MSB 2240 CCON=O. 240 MSB 2 2 5 0 CSPH=0.36 MSB 2 2 6 0 F V I S = O o 2 6 3 7 * E X P ( 7 3 6 2 o / 1 4 6 0 . + A T F 1 MSB 2 2 7 0

MSB 2 2 8 0 F D E N = 2 3 4 . 9 7 - O 0 0 2 3 1 7 * A T F MSB 2 2 9 0 FCON=0.70 MSB 2 3 0 0 FSPH=0.324 MSB 2 3 1 0

MSB 2 3 2 0 V I S K = ( C V I S / C V I S W ) * * 0 . 1 4 F V I S K = ( f V I S / F V I S W ) * * O . 14 MSB 2 3 3 0 D C V I S = C I A / C V I S MSB 2 3 4 0

MSB 2 3 5 0 QCCDEN = QC*CCDEN MSB 2 3 6 0

C CALCULATE REYNOLS AND PRANDTL NUMBER TUBE S I D E MSB 2 5 5 0 RENTO( I ) = D I A I * G T O / F V I S MSB 2 3 8 0 PRNTO( I l = F V I S * F S P H / F C O N MSB 2390

MSB 2 4 0 1 PDTO( I ) = ( . 0 0 2 8 + . 25*RENTO**L- .321 ) * E Q V B S C * G T 0 * ~ 2 * H E F I / MSB 2410

1 ( D I A I * F D E N * 4 1 7 1 8 2 4 0 0 o 1 MSB 2 4 1 1 MSB 2 6 4 0

GO TO 15 MSB 2 4 4 0 MSB 2 4 5 0

1 3 H T O ( 1 ) = FCON/DIA*~089*(RENTO(I~**06666~125. ) * ( P P N T O i I ) * * . 3 3 3 3 ) * MSB 2 4 6 0 1 F V I S K * H E F I * ( l . + o 3 3 3 3 s ( D E A E / T U B L N ( I I )**e66661 MSB 2 4 6 1 GO TO 15 MSB 2 4 7 0

14 H T O ( 1 ) = F C O N / D I A * ~ 4 ~ 3 6 + ~ 0 ~ 0 2 5 * R E N T O ~ I ~ * P R N T O ~ I ) ~ D I A I / T U B L N ~ I 1 MSB 2 4 8 0 1 ) / ( l . . + 0 ~ 0 0 1 2 * R E N T O ( I 1*PRNTO(11*DIAI/TUBLN(I)1 1 MSB 2 4 8 1

1 5 I F ( I o E Q o 1 ) G O TO 16 MSB 2 4 9 0 C CALCULATE FLOW AREAS SHELL S I D E MSB 2 4 8 0

V W O 1 ( I ) = QCCDEN/AWOl MSB 2 5 1 0 VW03( I 1 = QCCDEN/AW03 MSB 2 5 2 0 V M l ( I 1 = GSOlsCCDEN MSB 2 5 3 0 V M 2 ( I J = GS02*CCDEN MSB 2 5 4 0 V M 3 ( I ) = GS03sCCDEN MSB 2 5 5 0

FVISW=O. 2637*EXP ( 7 3 6 2 . / ( 4 6 @ o + F F T ) 1

CCDEN = l . /CDEN

MSB 2400 Cn I F ( KENTB E Q o 1 AND. R ENTO ( I GT. 1001 AND, I hE 1 1 w l H E F I = l . + ( ( R E N T O ( I ) - 1 0 0 @ 0 ) / 9 O O O o ) * * g o 5

C CALCULATE HEAT TRANSFER COEFF TUBE S I D E H T O ( I ~ ~ F C O N / D I A ~ ~ 0 2 1 7 * ~ R E N T O ~ I ~ * * ~ 8 1 * ~ P R N T O ~ I ~ ~ * o 3 3 3 3 ~ * F V I S K * H E f I MSB 2430

1 2 I F ( R E N T O ( I ) o L T o 2 1 0 0 . ) GC TO 14

C C A L C U L A T E PRESSURE DROPS S H E L L S I D E MSB 2590 D P 1 = (1.+.6*RB11*CDEN*VMl(I)**2 MSB 2570 D P 2 = .6*RBZ*CCEN*VM2( I 1**2 MSB 2580 D P 3 = ( l .+ .6 *RB3) *CDEN*VM3(1 ) * *2 MSB 2590

MSB 2600 R E N S O l ( I ) = G S O l * D C V I S R E N S 0 2 ( I) = G S 0 2 * D C V I S MSB 2610 R E N S 0 3 ( I ) = G S 0 3 * D C V I S MSB 2620 I F(KENTB.EQ. 1.AND. R E N S 0 2 ( I) GT. 1 0 0 1 . 1 MSB 2630

lHEFO=1.+0.3*( ( R E N S 0 2 ( 1 1 - 1 0 0 0 . 1/9000. 1**0.5 MSB 2631 P D S O ( 1 ) = (DPl+DP2+DP3)*PLK*HEF0/834624QOO* MSB 2640 I F ( I . E Q . 2 ) P D S O ( l 1 ~ P D S O ( 91 MSB 2650

C C A L C U L A T E B J FACTOR AND SHEL S I D E C O E F F I C I E N T MSB 2730 B J ( 1) = ( 0 * 3 4 6 * R E N S O l ( I ) * * ( - O 0 3 8 2 ) l * G B R L MSB 2670 B J ( 2 1 = ( O o 3 4 6 * R E N S 0 2 ( 1 1 * * ( - 0 o 3 8 2 ) ) *GBRL MSB 2680 B J ( 3 ) = ( O 0 3 4 6 * R E N S 0 3 ( 1 ) * * ( - 0 . 3 8 2 1 j * G B R L MSB 2690

MSB 2700 H S O 1 ( I 1 = ( L K * C S P H * G S O l * B J ( l I*( ( C C O N / ( C S P H * C V I S ) )** .661 ) * V I S K H S 0 2 ( 1 1 = ( L K * C S P H * G S 0 2 * B J ( Z ) * ( ( C C O N / ( C S ~ H * C V i S 1 ) ~ ~ o 6 6 ~ ) * V I S K MSB 2710

MSB 2720 AHSO( I 1 = ( ( ( H S O 1 ( I ) * S U M 1 1 + ( H S C Z ( I )*SUM2 1 +( H S 0 3 ( I )*SUM3 1 j / S N T ) *HEFO MSB 2730 GO T O 17 MSB 2740

16 PDSO( I ) = O m MSB 2750 APO=3.14 159* ( R A 8 2 - R A 5 2 ) -SNT*ATUBE MSB 2760

MSB 2770 GSO=QC/A PO MSB 2780 RENSO =GSO*DCVIS MSB 2790

MSB 2800 P R E S 0 =CVIS*CSPH/CCON MSB 2810

1 +PRES0 * * 0 * 3 3 / D I A MSB 2 8 1 1 MSB 282@

A = QF*FSPH MSB 2830 B = QC*CSPH MSB 2840 D = UOA( I ) * S N T * B S O * 3 . 1 4 1 5 S * D I A MSB 2850 P = -HSFCT* (D* (A-B) ) / ( A * B )

MSB 2870 P B A R = E X P ( P 1 MSB 2880 C = ( 8 - A ) * P B A R

T C O ( I ) = ( ( T C I ( I l * ( B * P B A R - A 1 1 - ( T F C ( I ) *A* (PBAR- l . 1 1 )/C MSB 2890

(r .P

H S 0 3 ( I ) = ( & K * C S P H s G S 0 3 * B J ( 3 J * ( ( C C O N / ( C S P H * C V I S ) 1 * * * 6 6 ) ) * V I S K

EQV D I A = 4 .*APO/ ( 3 14 159* SN T*D I A+6 243 18* 4 RA8+RA5 1 I

A H S O ( I ) = O . l 2 8 * C C O N * V I S K * ( 1 2 o * € Q V D ~ A * R E N S O )**0.6

17 U O A ( I )=1 e o / ( ( l , O / A H S O ( I 1 1 + ( l . O / H T O ( I 1 I + (1 . O / H k l )

MSB 2900 T F I ( 1 I = ( ( T C O ( I ) - T C I ( I ) ) * B / A J + T F O ( 1 ) H E A T ( 1 ) = - A * ( T F I ( I J - T F O ( 1 ) ) MSB 2910

MSB 2920 MSB 2930 C T I F = T f I ( I ) - T F O ( I )

C T I C = T C O ( I I - T C I ( 1 ) MSB 2940

T I F = C T I F MSB 2960 MSB 2970 T I C = C T I C MSB 2980 KEY 5=K EY 5+ 1 MSB 2990 MSB 3000 GO TO 11

1 8 THEATO = THEATO + H E A T ( 1 ) MSB 3010 MSB 3020 TPDTO = TPDTO + P D T O ( 1 I MSB 3030 TPDSO = TPDSO + PDSO(1) MSB 3040 MSB 3090 MSB 3100

TWDT( I) = ( H E A T ( I) I N T O 1 *ALOG ( D I A / D I A I 1 / ( 2 * 0 * 3 . 14159*BSO*WCOND)

I F( I ABS ( CT I F-T I F 1 L E ( 3 0 1 1 AND. (ABS ( C T I C - T I C 1 LE. ( 3 0 0 1 1 GO T 0 1 8 MS B 2950

I F ( K E Y 5 . G T . 5 0 ) G O TO 3 7

I F ( I EQ 2 1 TPDSO=TPD SO+PDSO ( 1 1 C D T F = ( ( ( H E A T ( I ) ) / N T O ) / B S O ) / ( 3 . 1 4 1 5 9 * D I A * A H S C ( I J ) F D T F = C D T F * A H S O ( I 1 / H T O ( I 1 FWT ( 11 =ATF-FDTF*HSFCT CWT( I ) =ATC+CDTF*HSFCT

MSB 3130 MSB 3140 TSUM=TSUM+AVWT( I) MSB 3150 S SUM=SSUM+ATC MSB 3 0 5 0

I F ( ( ( A B S ( E T F - T F I ( 1 ) ) ) . L E * ( ( A B S ( T F I ( I ) - T F O ( I ) I ) / 2 * 0 ) 1. OR. MSB 3060 MSB 3061

I=I+l MSB 3070 MSB 3 0 8 0 MSB 3160 MSB 3170 T F O ( 1 ) = T F I ( 1 - 1 1 MSB 3180 T C I ( 1 ) = T C O ( 1 - 1 1

B S O = B S O I MSB 3190 MSB 3200 E Q V B SO = B SO

K EY4=KEY 4+ 1 MSB 321@ MSB 3220 IF(KEY4,GT.SO)GO TO 3 6 MSB 3230 GO TO 10 MSB 3240 19 K F I N A L = l

I T = I MSB 3250 MSB 3260 F I T = I T

m Ln

AVWT 4 I 1 = O . 5* ( F WT ( I) +ChT ( I I 1

I F( K F I N A L . EQ 1 .AND I EQ I T I GO TO 20

1 ( T F I ( I ) . L E . E T F ) I GO TO 15

I F ( I . G T . 7 5 ) GO TO 30 I F ( I.EQ.21 A T C l Z A T C

DCURVE=CURVES*((HEATL-THEATO)/HEAT(l)l CURVES=CURVES+DCURVE GO TO 9

2cI TUBLEN=( F I T - 1 . ) *BSOI+CURVES HEXLEN=( F I T - 1 . ) * B S 0 1 + 4 . * E X P R A D * S I N ( A R C R ) +DCURVE+Oo25*BSMAX STRLEN=( F I T - 1. )*BSOI+DCURVE+. 2 5 * B S M A X

2 1 I F ( KTBST.EQ.0) GO TC 2 4 T l = F W T ( 1 ) TZ=CWT( 1) P D T O l = P D T O ( 1 1 P D S O l = P D S O ( l ) TSUM=TSUM-AVWT ( 1 ) S SUM =S S U M- A T C 1 T A V T = ( CURVES*AVWT( 1 )+BSOI*TSUM) / T U B L E N SAVT=( ( H EXLEN-BSO I * ( F 11-1 1 1 *ATC 1+B SOI*SSUly) /HEXLEN C A L L T U B S T R ( T P I N . SPOUT, PDTO1 r P D S O L , T P D S O v T l r T 2 r

1 2 3 4 5 8 8 3 r B B 4 r B B 5 ~

HEXLENr E X P R A D v D I A I r D I A ,ARC, E T F r F T O r ETC r C T O r S A V T r T A V T 9

T 1 1 r T 1 2 r T 1 3 r T 2 4 r T 2 5 r T 3 6 9 T 3 7 . 1 3 8 r T 4 9 r T 4 1 Q r O T r B F r A S M 9

S T r STP 9 SQP, SLPR 9 S L P G r S L L O r S L L I 7 STTO r S T T I r T M r CASMrCTM P 1 r P 2 r SA. R 1 r R 2 , T L .RBI A A l r A A 2 r AA3 r A A 4 r A A 5 r B El 9 882 r

K E Y 3=K EY 3+ 1 I F ( K E Y 3 . G T . 5 0 ) G O T O 35 I F ( T 2 4 . L T . O . O ~ O R . T l 2 ~ L T o O o O ) GO TO 2 2 I F ( T 2 4 . G T . ( . 0 8 ~ A S M ) . A N D ~ T l 2 . G T . ( . @ 8 ~ A S M ~ ) GO T O 2 3 GO T O 2 4

22 XPRMIN=EXPRAD GO TO 8

23 XPRMAX=EXPRAD GO TO 8

24 VOL = 0 .7854* (D IA I * *2 .O) *NTO*TUBLEN C CHECK OF TUBE AND S H E L L PRESSURE DROPS

K E Y 2 = K E Y 2 + 1 IF(PERCZ.LE.O.1) GO TO 33 I F ( T P D T O . L T o ( P E R C Z * P R D T ) ) GO TO 2 5 IF(TPDTO.GT.PRDT1 GO TO 2 6 GO TO 27

MSB 3270 MSB 3280 MSB 3290 MSB 3300 MSB 3310 MSB 3320 MSB 3330 MSB 3340 MSB 3350 MSB 3360 MSB 3370 MSB 3380 MSB 3390 MSB 3400 MSB 3410 MSB 3420 MSB 3421 MS0 3422 MSB 3423 MSB 3424 MSB 3425 MSB 3430 MSB 344@ MSB 3450 MSB 3460 MSB 3470 MSB 3480 MSB 3490 MSB 3500 MSB 3510 MSB 3520 MSB 3250 MSB 3540 MSB 3550 MSB 3560 MSB 3570 MSB 3580

cn cn

2 5

26

27

28

29

C C

30

I F ( R A 8 * L E . ( R A 5 +0 .005) ) GO TO 34 R A 8 H =RA8 I F ( K E Y 2 . N E . 3 0 ) G O TO 3

P E R C 2 = PERC2 - @ . C l K E Y 2 = 1 0 GO TO 3

R A 8 L =RAE?

RA8LzRA8L-C. 2

I F ( R A 8 . G E . ( R A 8 M A X - C ~ 0 0 5 J ) GO TO 34

I F ( K E Y 2 e N E . 3 0 ) GO TO 3 RA8H=RA8H+Oo2 PERC2 = PERC2 - 0.01 K E Y 2 = 1 0 GO TO 3 K E Y 1 = K E Y 1 + 1 I F ( P E R C l . L E o O . 1 J GO TO 32 IF(TPOSO.CTo(PERCl*PRDS)l GO TO 2 8 IF(TPDSO.GT.PRDS)GO TO 2 9 GO TO 38

BSH = B S O I I F ( BSO I LE. ( BSMIN+0.005 1 )GO TO 3 1

I F ( K E Y L * N E * 3 0 1 G O TO 2 BSL=BSL-Oo 1 P E R C l = P E R C l - 0.01 K EY 1=10 GO TO 2

B S L = B S O I I F ( B SO I G E ( B S MA X- 0 0 0 5 1 1 GO TO 3 1

I F ( K E Y l o N E o 3 0 ) GO TO 2 BSH=BSH+O. 1 P E R C l = P E R C l - 0.01 K E Y 1 = 1 0 GO TO 2

MSB 3590 M S B 3600 MSB 3610 M S B 3620 M S B 3630 M S B 3640 M S B 3650 MS0 3660 MSB 3670 M S B 3680 M S B 3690 M S B 3700 MSB 3710 M S B 3720 M S B 3730 MSB 3760 M S B 3770 M S B 3780 M S B 3790 MSB 3800 MSB 3810 M S B 3820 M S B 3830 M S B 3840 MSB 3850 MSB 3860 MSB 3870 M S B 3880 M S B 3890 MSB 39CO MSB 3910 M S B 3920 MSB 3930

m 4

M S B 3640 P R I N T E X I T S I G N A L S M S B 3650 P R I N T 1 0 5 1 t B S O MSB 3960

GO TO 38 MSB 3980 1057 F O R M A T ( 3 9 H l B A F F L E SPACINGS EXCEEDE 7 5 W I T H B S C = t F 5 0 2 r Z X t 4 H ( F T ) ) MSB 3970

3 1 P R I N T 1 0 5 2 1058 F O R M A T ( 2 C H l B S O I = MAX. OR M1N.I

GO TO 38 3 2 P R I N T 1059 1C59 F O R M A T ( 4 8 H l P E R C 1 FOR SHELL PRESSURE DROP IS L E S S T H E & 0.1)

GO T O 38 33 1C. 60

34 106 1

35 106 2

36 1@ 63

37 1064

C C

3 8

39

P R I N T 1060

GO TO 38 P R I N T 1061

GO TO 38

F O R M A T ( 4 8 H l PERC2 FOR TUBE PRESSURE DRGP IS L E S S T H E N 0.11

F O R M A T ( 2 9 H l SHELL R A D I U S = MAX, CR MIN.1

P R I N T 1062, K E Y 3 FORMAT( 6 H l K E Y 3 = 9 I 5 1 GO TO 3 8 P R I N T 1063, K E Y 4 F O R M A T ( 6 H l K E Y 4 z , 1 5 1 GO TO 3 8 P R I N T 1 0 6 4 , K E Y 5 FORMAT( 6 H l K E Y 5 = 9 I5 1 GO TO 38

END OF CASE, P R I N T OUTPUT DO 39 I = l r I T V l ( 1 I = V M l ( I ) * G F T T V 2 ( 1 ) = V M 2 ( I I * G F T T V 3 ( I J = V M 3 ( I 1*GFTT VW1( I 1 = V W O l ( I 1*GFTT VW3( 1) = VW03( I I * G F T T C O N T I N U E TTDSO = TPDSO*GFT T T D T O = TPDTO*GFT

SPPERC=TPDSO*lOO./PRDS HTP ERC= 100 .* TH EA TO /HE A T L

T P P ERC=TPDTO*lOO./PRDT

AR E A = 3 1 4 1 59*D I A * SNT* TUBL EN

MSB 3990 MSB 4000 MSB 4010 MSB 4020 MSB 4030 MSB 4040 MSB 4050 MSB 4 C 6 0 MSB 4070 MSB 4 C 8 0 MSB 4090 MSB 4100 MSB 4110 MSB 4120 MSB 4130 MSB 4140 MSB 4150 MSB 4160 MSB 4170 MSB 4180 MSB 4190 MSB 381@ MSB 3820 MSB 4220 MSB 4230 MSB 4240 MSB 4250 MSB 4260 MSB 4270 MSB 4280 MSB 4290 MSB 4300 MSB 4310 MSB 4320 MSB 4330 MSB 4340

m co

*

ASM3=3. *ASM MSB 4350 P STO=AA 1 MSB 4360 PQSTO=AA2 MSB 4370 PQFSTO=AA3 MSB 4 3 8 0 P S T I = B B l MSB 4390 P Q S T I = B B 4 MSB 4400 P Q F S T I = B B 5 MSB 4410

C MSB 1640 P R I N T 1033,TPEATO,HTPERC MSB 4430

P R I N T 1 0 3 5 9 QF MSB 4450 P R I N T 1@36,TTDSO,SPPERC MSB 4460 P R I N T 1037, TTDTO, TPPERC MSB 4470 P R I N T 1 0 3 8 r R A 8 MSB 4 4 8 0 P R I N T 1 0 3 9 r B S O I MSB 4490 P R I N T 1 0 4 0 r V C L MSB 4 5 C 0 P R I N T 1041, AREA MSB 4510

P R I N T 10 43 9 TUBL EN MSB 4530 P R I N T 1044, HEXLEN MSB 4540 P R I N T 1045, STRLEN MSB 4 5 5 0 P R I N T 1 0 4 6 v E X P R A D MSB 4560 P R I N T 1 0 4 7 ~ GBRL MSB 4 5 7 0 P R I N T 1 0 5 1 VTAVT MSB 4 5 8 0 P R I N T 1 @ 5 2 9SAVT MSB 4590 P R I N T 10 539 P STO, P S T I I A S M MSB 4600 P R I N T 1 0 5 4 t P Q S T O q P Q S T I r A S M 3 MSB 4610 P R I N T 1055,PQFSTO,PQFSTI,SA MSB 4620 P R I N T 1 0 4 8 , ( I , ( T C I ( I J , T C O ( I J r C W T ( 1 I T T F I (I J , T F C ( I J r F h T ( I ) v MSB 4630

1 T W D T ( I 1 I r I = l * I T ) MSB 4631

1 I = l , I T I MSB 4641

1HTO( I 1 ,AHSO( I J MSB 4651 C MSB 4 2 4 0 C LOOP FOR A D D I T I O N A L CASES I F R E Q U I R E D MSB 4 2 5 0 40 C O N T I N U E MSB 4 6 8 C

P R I N T 10349 QC MSB 4440

P R I N T 1 0 4 2 r S N T MSB 4 5 2 0

P R I N T 1 0 4 9 9 ( I , ( V l ( I ) , V 2 ( 1 ) r V 3 ( I J t V W l ( 1 1 r V W 3 ( I J ,PCSO(I ),PDTO( I ) J , MSB 4640

P R I N T 1@5Q,(Ir(RENTO(I)rPRNTO(I)tRENSOl(I J r R E h S C 2 ( I ) r P E N S 0 3 ( I J , MSB 4650 ,UOA( I 1 * H E A T ( 1 ) 1 t I = l v I T )

m W

K E Y 7 = K E Y 7+ 1

GO TO 1 41 CONTINUE

END

I F ( K E Y 7 o G T m K A S E S ) G O TO 4 1 MSB 4690 MSB 4700 MSB 4710 MSB 4720 MSB 4730

SUBROUTINE TUBSTR(TPINvSPOUT~PDTCl~PDSOl~TPDSOvTlvT2v TUBST 10 1 HEXLENv E X P R A D v D I A I t D I A ,ARC, E T F v F T O t ETC v C T O v SAVTvTAVT v TUBST 11 2 T l l , T 1 2 ~ T 1 3 v T 2 4 v T 2 5 v T 3 6 v T 3 7 v T 3 8 v T 4 9 v T 4 l O v D T v e ) Y v A S M v TUBST 12 3 S T ~ S T P ~ S Q P ~ S L P R ~ S L P G v S L L O ~ S L L I ~ S T T O ~ S T T I v T M v C A S ~ v C T M v TUBST 13 4 P l v P 2 v S A v R 1 9 R 2 , TL ,RB v A A l v A A 2 vAA3 v A A 4 v A A 5 v B B l r B B 2 v TUBST 14 5 B B 3 r B B 4 , B B 5 ) TUBST 15

D I M E N S I O N C A S M ( 6 r C T M ( 6 1 TUBST 20 G F T = 1 ./ 144 TUBST 30 P 1 = ( T P I N - . 5*PDTO1 l * G F T TUBST 40 P 2= ( SPOUT + a 5*PDSO1 ) * G F T TUBST 50 R 1=6 * D I A I TUBST 60 R 2 = 6 * D I A TUBST 70 T L =12.*HEXLEN TUBST 80 RB= lZ . *EXPRAD TUBST 90 A=!Io017452*ARC TUBS 100

cc DETERMINE AVERAGE CHANGE I N TEMPERATURE OF S H E L L ( D T S 1 AND T U B E ( D T T 1 110 DTS = S A V T - 7 0 0 TUBS 120 DTT T A V T - 7 0 . TUBS 130

DP = P l - P 2 TUBS 150 DT = T l - T Z TUBS 160

TUBS 170 TM = ( T l + T 2 ) / 2 . TUBS 1 8 0

4 0

c c CALCULATE PRESSURE AND TEMPERATURE D I F F E R E N T I A L ACROSS T U B E MALL. TUBS 140

cc AND AVERAGE TEMPERATURE OF T b B E kALL

cc C A L C U L A T E MOMENT OF I N E R T I A OF TUBE C R O S S E C T I C h ( A H 1 )

cc C A L L SUBROUTINE TO DETERMINE A L L C k A B L E S T R E S S ( A S V )

cc E S T A B L I S H M A T E R I A L P R O P E R T I E S COhSTANTS

A M I = O o 7 8 5 3 S 8 * ( R 2 * * 4 - R 1 * * 4 )

C A L L LAGR (CASMT CTMqASM t T M t 2 T 6 T I E R R )

SA= 25000.r) EM = 25COOOOO.O PR = 003 T E = OoCOOOO78 S E = CoOCOOO76

c c C A L C U L A T E A X I A L LOAD AND MOMENT DUE TO L G N G I T U C h A L E X P A N S I O N DY = T L * ( TE*DTT-SEWTS I

TW = R 2 - R 1 A L = TW*RB/RM**2 A L 2 = AL**2

RM = ( R 2 + R 1 ) / 2 o

AK = ( l . + 1 2 o * A L 2 ) / ( 1 0 o + l Z o * A L Z ) A A = 2o*A P = BM = P * R B * ( l o - C O S ( A ) I

2 5@00OOO *AK*AM I *DY / ( RB **3* 4 AA*C 0 S ( AA ) -3 *S I h ( A A 1 +4. * A 1 I

cc C A L C U L A T E Q ZTRESS DUE TO P

cc C A L C U L A T E Q STRESS DUE TO M SQP = -P/( 6.28318*RM*Tk I

B l = 6o/ (5 .+6 . *AL21 6 2 = B M / ( A K * A M I ) 63 = ( R 2 / R M ) * * 2 64 = ( R l / R M ) * * 2 85 = 1.5*RM*BZ*AL*Bl S L L O = R 2 * B 2 * ( l . - B l * B 3 ) S L L I R l * B 2 * ( 1 o - B 1 * B 4 ) STTO = 6 5 * ( 1 o - Z o * B 3 1 S T T I = B5*(1 . -2 . *84)

cc C A L C U L A T E F STRESS DUE TO TUBE WALL TEMPERATURE CROP ST = 1 3 S o * D T S L I = -ST S T I = -ST S L O = S T STO = S T

T U B S 190 T U B S 200 T U B S 210 T U B S 220 TUBS 230 T U B S 240 T U B S 250 T U B S 260 TUBS 270 T U B S 280 TUBS 290 TUBS 300 T U B S 310 T U B S 320 T U B S 330 TUBS 340 T U B S 350 TUBS 360 T U B S 370 TUBS 380 TUBS 390 T U B S 400 T U B S 410 T U B S 420 T U B S 430 TUBS 440 T U B S 450 T U B S 460 TUBS 470 T U B S 480 T U B S 490 T U B S 500 TUBS 510 T U B S 520 T U B S 530 T U B S 540 T U B S 550 T U B S 560

4 w

cc cc

cc

cc

cc

cc

cc

cc cc cc cc

cc

C A L C U L A T E STRESSES DUE TO PRESSURE HOOP S T P = DP*RM/TW LONG I T U D N A L

S L P G = 0 R A D I A L S R P I = - P 1 SRPO = - P 2 P STRESS T U B E OD BEND OD

S L P R = S T P / 2 .

A l l A 1 2

= A M A X l ( STP 9 SLPRI SRPC) = A M I N l ( STP 9 SLPRI SRPC)

A A 1 = A l l - A 1 2 T 1 1 = ASM- A B S ( A A 1 J P+Q STRESS T U B E OD BEND OD A 1 3 A 14

= A M A X l ( STP+STTO 9 SLPR+SQP+SLLC VSRPOJ =AM I N 1 ( STP+STTO 9 SLPR+ IQP+SLLC! 9 SR P O )

A A 2 = A l 3 - A l 4 T 1 2 = 3*ASM- A B S ( A A 2 )

A 15 A 1 6

P+Q+F STRESS TUBE OD BEND OD =AMAX1 ( STP +STTO+STO 9 SLPR+ SQP+ S L L O+ SLO 9 SRPC I = A M I N 1 ( STP+STTO+STO 9 SLPR+ SQP+SLLO+SLO (SRPC)

A A 3 = A 1 5 - A 1 6 T 1 3 = SA - A B S ( A A 3 ) P STRESS T U B E OD BEND I D SAME AS P STRESS A T TUBE CD BEND OD -- T 1 1 )

P+Q STRESS T U B E OD BEND I D A 2 2 = A M A X l ( STP+STTO, SLPR+SQP-SLLCrSRPOI A 2 3 = A M I N l ( STP+STTO* SLPR+SQP-SLLOvSRPO) A A 4 = A 2 2 - A 2 3 T 2 4 = 3*ASM- A B S ( A A 4 J P+Q+F STRESS T U B E OD BEND I D A 2 4 =AMAX1 ( STP+STTO+STO,SLPR+SQP-SLLO+SLO1SRPO) A 2 5 =AM I N 1 ( STP +STTO+STO 9 SLPR+ SQP-SL LO+ SLO 9 S R P C ) A A 5 = A 2 4 - A 2 5 T 2 5 = SA - A B S ( A A 5 )

T U B S 570 TUBS 580 TUBS 590 T U B S 600 TUBS 610 TUBS 620 TUBS 630 T U B S 640 TUBS 650 TUBS 660 TUBS 670 TUBS 680 T U B S 690 T U B S 700 T U B S 710 TUBS 720 TUBS 730 TUBS 740 T U B S 750 TUBS 760 T U B S 770 TUBS 780 TUBS 790 TUBS 800 T U B S 810 T U B S 820 T U B S 830 T U B S 840 TUBS 850 T U B S 860 TUBS 870 T U B S 880 TUBS 890 TUBS 900 T U B S 910 T U B S 920 T U B S 930

4 h)

I . #

cc

cc

cc

cc cc cc cc

cc

cc

P STRESS T U B E I D BEND OD 811 = A M A X l ( S T P T S L P R * S R P I j 812 = A M I N ~ ( S T P T S L P R * S R P I I B B l = B 1 1 - 6 1 T 3 6 = ASM- A B S ( B B 1 ) P+Q STRESS T U B E I D BEND OD B 13 =AMAX1 ( SJP+STT I * SLPR+ SQP+SLL I T S R P I 1 814 = A M I N l ( S T P + S T T I * S L P R + S Q P + S L L I I S R P I ) B B 2 = 813-814 T37 = 3*ASM- A B S ( B B 2 ) P+Q+F STRESS T U B E I D BEND OD 8 1 5 B 1 6

S A M A X l L S T P + S T T I + S T I r S L P R + S Q P + S L L I + S L I T S R P I 1 = A M I N l ( S T P + S T T I + S T I p S L P R + S Q P + S L L I + S L I T S R P I 1

883 = B l 5 - 8 1 6 T 3 8 = SA - A B S ( B B 3 ) P STRESS T U B E I D BEND I D S A M E AS P STRESS AT TUBE ID BEND OD -- T 3 6

P+Q STRESS T U B E I D BEND I D 823 = A M A X l ( S T P + S T T I * S L P R + S Q P - S L L I r S R P I j

824 = A M I N l ( S T P + S T T I T S L P R + S Q P - S L C I T S R P I I 884 = 823-824 T 4 9 3*ASM- A B S ( B B 4 1 P+Q+F STRESS T U B E I D BEND I D 825 826 885 = 8 2 5 - 8 2 6 T 4 1 0 = S A - A B S ( B B 5 l

= A M A X l ( Z T P + S T T I + S T I T S L P R + S Q P - S L L I + S L I r S R P I 1 =AM I N l ( STP+STT I + S T IT SLPR+SQP-SCLI+ S L I T S R P I 1

cc c c

RETURN END

TUBS 940 TUBS 950 TUBS 960 TUBS 970 TUBS 980 TUBS 990 T U B 1000 T U B 1010 T U B 1020 T U B 1030 T U B 1040 T U B 1050 T U B 1060 T U B 1070 T U B 1080 T U B 1090 T U B 1100 T U B 1110 T U B 1120 T U B 1130 T U B 1140 T U B 1150 T U B 1160 T U B 1170 T U B 1180 T U B 1190 T U B 1200 T U B 1210 T U B 1220 T U B 1230 T U B 1240 T U B 1250 T U B 1260

4 w

C C C C C C C C C C C

1

2 C

3 4

5

6 C

7

C 8

SUBROUT I N E LAGR D I M E N S I O N F X ( N P 7 1 , X ( N P T )

( F X T X 9 F X P r X P T N T N P T t I E R I

SUBROUTINE U S E S L A G R A N G I A N I N T E R P O L A T I C N T C A D E S I R E D DEGREE P O L I N O M I AL F X = F U N C T I O N OF INDEPENDENT V A R I A B L E X = I N D E P E N T E N T V A R I A B L E F X P = E S T I M A T E OF F X A T XP XP = VALUE OF X FOR WHICH I N T E R P O L A T I C N I S D E S I R E D N = DEGREE OF P O L I N O M I A L USED I N I N T E R P C L A T I C h NPT = NUMBER O F P O I N T - P A I R S I N T A B L E I E R = COUNTER TO REPORT TYPE OF E X E C U T I C N

CHECK T O SEE I F XP I S A T A B L E ENTRY DO 2 K = l 9 N P T I F ( XPeEQ o x ( K ) 1 1 9 2 F X P = F X ( K ) I E R = 3 RETURN C O N T I N U E D E T E R M I N E I F E X T R A P O L A T i C h I S REQUIRED I F ( X P o L T .X( 1 ) 14.3 I F ( X P o G T e X ( N P T 1I 59 6 L 1 = 1 L 2 = N P T GO TO 1 5 L 1 = N P T - N L 2 = NPT GO TO 15 I E R = 2 D E T E R M I N E I F S U F F I C I N T DATA IS PRESENT FOR DEGREE OF P O L I N O M I A L M = N + l

I E R = 1 RETURN D E T E R M I N E NEXT H I G H E S T P O I N T

K 1 = K

I F ( M GT e NPT ) 7 9 E

DO 9 K = 2 9 N P T

I F( XP LT 0x4 K ) I 1099

LAGR 10 LAGR 20 LAGR 30 LAGR 40 LAGR 50 LAGR 60 LAGR 70 LAGR 80 LAGR 90 LAGR 1OC LAGR 110 LAGR 120 LAGR 130 LAGR 140 LAGR 150 LAGR 160 LAGR 170 LAGR 180 LAGR 190 LAGR 200 LAGR 210 L A G R 220 LAGR 230 LAGR 240 LAGR 250 LAGR 260 LAGR 270 LAGR 280 LAGR 290 LAGR 3CO LAGR 310 LAGR 320 LAGR 330 LAGR 340 LAGR 350 LAGR 360 LAGR 370 LAGR 380

9 c

10 11

12

13

14

C C

15

16

17 18

CONTINUE LAGR DETERMINE THE LOWER POINTS REQUIRED LAGR L = M/2 LAGR L2 = Kl + L - 1 LAGR IF(LZ.LE.NPT~13,12 LAGR Kl =Kl-1 . .

LAGR GO TO 11 LAGR Ll = Kl + L - M LAGR IF(LlJ14,14,15 LAGR Kl = Kl + 1 LAGR L2 = L2 + 1 LAGR GO TO 13 LAGR INTERPOLATION BY LAGRANGIAN METHCD (SEE MATHEMATICS OF PHYSICS LAGR AND MODERN ENG INEER ING , SOKOLNIKOFF AND REDHEFFER rPAGES 699,700)LAGR FXP = 0.0 LAGR DO 18 K = LlrL2 LAGR PKX = 1.0 LAGR PKXK = 1.0 LAGR DO 17 I = LlrL2 LAGR IF(I.EQ.K)17,16 L AGR PKX = PKX*(XP - X( I )1 LAGR PKXK = PKXK*LX(K) - X(I)) LAGR CONTINUE LAGR FXP = FXP + FX(K)*PKX/PKXK LAGR RETURN LAGR END LAGR

390 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640

76

In te rmedia te Var iab les

L A W 0 1

LAW03

NT (1)

BJ( I )

HSOl ( I )

HS02 ( I )

HS03 (I)

N e t c ross - f low circumference a t i nne r edge of b a f f l e , f t .

Net c ross - f low circumference a t o u t e r edge o f b a f f l e , f t .

Number o f tubes i n r i n g I.

J f a c t o r f o r the h e a t t r a n s f e r c o e f f i c i e n t a t t he i n n e r window zone (I = l ) , cross-f low zone (I = 2 ) , and o u t e r window zone

S h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t f o r i nne r window zone i n increment I , Btu/hr.ft'. O F .

S h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t f o r c ross - f low zone i n increment I .

S h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t f o r o u t e r window zone i n increment I .

( I = 3 ) .

TUBLN(1) Accumulated tube l eng th up t o increment I , f t .

Average v e l o c i t y of f l u i d i n outer window zone i n increment I, f t l s ec .

Average v e l o c i t y of f l u i d i n over lapping b a f f l e zone i n i n c r e - ment I .

Average v e l o c i t y of f l u i d i n i n n e r window zone i n increment I .

F lu id v e l o c i t y ac ross tubes i n o u t e r edge of b a f f l e i n i n c r e - ment I , f t / s e c .

F lu id v e l o c i t y ac ross tubes i n inne r edge of b a f f l e i n i n c r e - ment I .

Ins ide c r o s s - s e c t i o n a l a r ea of tube , f t 2 .

F lag f o r number of i t e r a t i o n s on b a f f l e spac ing .

F rac t ion of i npu t s h e l l - s i d e p re s su re drop considered acceptab le .

Flag f o r number of i t e r a t i o n s on o u t e r r a d i u s .

F rac t ion of i npu t tube-s ide pressure drop considered accep tab le .

Current lower l i m i t f o r o u t e r r a d i u s .

Current h ighe r l i m i t f o r o u t e r r ad ius .

Temporary number of tube r i n g s .

I n t e g e r form of RJ8.

Real form o f 158.

Radius of tube r i n g I , f t .

Circumference of tube r i n g I , f t .

Temporary c i r cumfe ren t i a l p i t c h i n tube r i n g I , f t .

7 7

TOTAL(1) Accumulated number of tubes up t o tube r i n g I.

AVWT(1) Average temperature of tube w a l l i n increment I , OF.

KEY7

HEFI

HEFO

HS FCT

ARCR

ATUBE

GFTT

GFT

D I A I

58

TRPI

CPI

NTO

RA5 2

RA8 2

RA6

J6

RA7

57

RA6 2

RG7 2

€31

RB2 RB3 SUM1

SUM2

SUM3

Ism1 Ism2 ISUM3

BSMAX

BSMIN

F lag f o r number of cases performed.

Tube-side enhancement f a c t o r .

S h e l l - s i d e enhancement f a c t o r .

Flag: 1 = tube s i d e h o t t e r than s h e l l s i d e , -1 = tube s i d e co lde r than s h e l l s i d e .

Arc o f ben t tube f o r thermal expansion, r ad ians .

Outside c r o s s - s e c t i o n a l a r ea of tube , f t 2 .

1/3600 . 1/144 . I n s i d e diameter of tube , f t .

Actual number of tube r i n g s .

Actual r a d i a l p i t c h , f t .

Actual c i r cumfe ren t i a l p i t c h , f t .

I n t e g e r form of TOTAL(1).

Square of R A ~ , f t 2 .

Square of M a , f t 2 .

Radius of i nne r b a f f l e edge, f t .

Number of tube r i n g s up t o RA6.

Radius of o u t e r b a f f l e edge, f t .

Number of tube r i n g s up t o RA7.

Square of RA6, f t2 .

Square of R A ~ , f t 2 .

Number of tube r i n g s i n inne r window zone.

Number of tube r i n g s i n c ross - f low zone.

Number of tube r i n g s i n o u t e r window zone.

Number of tubes i n inne r window zone.

Number of tubes i n cross-f low zone.

Number of tubes i n o u t e r window zone.

I n t e g e r form of SUM1.



Higher l i m i t f o r b a f f l e spac ing , f t .

Lower l i m i t f o r b a f f l e spacing, f t .

78

APO 1

A P 0 3

Hw CSPHAV

FSPHAV

GTO

KEY3

XPRMAX

XPRMIN

BSH

BSL

CURVES

I T

KFINAL

TSUM

SSUM TPDTO

TPDS 0

TIF

T I C

CDTF

FDTF

BSO

GB RL

AWO 1

AW03

A w l

AW2

AW3

G S O l

GS02

GS 03

EQVBSO

N e t p a r a l l e l flow i n i n n e r window zone, f t 2 .

N e t p a r a l l e l flow i n o u t e r window zone, f t 2 .

Heat t r a n s f e r c o e f f i c i e n t ac ross tube w a l l , Btu/hr*ft'.OF.

Average s p e c i f i c h e a t i n s h e l l s i d e , B tu / lb*"F .

Average s p e c i f i c h e a t i n tube s i d e .

Mass flow r a t e i n tubes, l b / h r - f t 2 .

Flag f o r number of i t e r a t i o n s on tube expansion r a d i u s .

Higher l i m i t on tube expansion r a d i u s , f t .

Lower l i m i t on tube expansion r a d i u s , f t .

Current h ighe r l i m i t f o r b a f f l e spacing, f t .

Current lower l i m i t f o r b a f f l e spacing, f t .

An approximate l eng th of the curved s e c t i o n of the tubes , f t .

Number of b a f f l e spacings.

A f l a g t o i n d i c a t e t h a t t he h e a t load requirement has been m e t .

Accumulated average temperature of tube w a l l .

Accumulated average temperature of s h e l l f l u i d .

Accumulated tube-side p re s su re drop.

Accumulated s h e l l - s i d e p re s su re drop.

Assumed temperature d i f f e r e n c e i n tube-side f l u i d between two increments, OF.

Assumed temperature d i f f e r e n c e i n s h e l l - s i d e f l u i d between two increments, OF.

Tube-side bulk t o w a l l temperature d i f f e r e n c e , O F .

S h e l l - s i d e bulk t o w a l l temperature d i f f e r e n c e , OF.

Current b a f f l e spacing, f t .

Correct ion f a c t o r f o r Be rge l in ' s h e a t t r a n s f e r c o e f f i c i e n t .

Net cross-f low a r e a a t i n n e r edge o f b a f f l e , f t 2 .

Net cross-f low a r e a a t o u t e r edge of b a f f l e , f t 2 .

E f f e c t i v e flow a r e a i n i n n e r window zone, f t 2 .

E f f e c t i v e flow a r e a i n cross-f low zone, f t 2 .

E f f e c t i v e flow a r e a i n o u t e r window zone, f t 2 .

Mass flow r a t e i n i n n e r window zone, l b / h r . f t 2 .

Mass flow r a t e i n cross-f low zone, l b / h r . f t 2 .

Mass flow r a t e i n o u t e r window zone, l b / h r . f t2.

Length of h e a t exchanger i n the curved tube region considered a s f i r s t b a f f l e spacing.

J

7 9

W

W

KEY4

KEY5

ATC

CFT

ATF

FFT

F I

CVIS

CVISW

CDEN

CCON

CS PH

FVIS

FVISW

FDEN

FCON

FS PH

VISK

FVISK

DCVIS

CCDEN

QCCDEN

DP 1

DP2

DP3

APO

EQVDTA

GS 0

RENSO

PRES0

CTIF

C T I C

I n a c t i v e .

F lag f o r number of i t e r a t i o n s on average temperature i n each b a f f l e spacing.

S h e l l - s i d e average temperature i n each b a f f l e spac ing , OF.

Average tube w a l l temperature on s h e l l s i d e i n each b a f f l e spac ing , OF.

Tube-side average temperature i n each b a f f l e spac ing , OF.

Average tube w a l l temperature on tube s i d e i n each b a f f l e spac ing , OF.

Number of b a f f l e spaces .

S h e l l - s i d e f l u i d v i s c o s i t y , l b / f t . s e c .

CVIS eva lua ted a t wa l l temperature.

S h e l l - s i d e f l u i d d e n s i t y , l b / f t3 .

She l l - s ide f l u i d conduc t iv i ty , B t u / h r . f t . OF.

S h e l l - s i d e f l u i d s p e c i f i c h e a t , B tu / lb* OF.

Vi scos i ty of tube-side f l u i d , l b / f t . s e c .

FVIS eva lua ted a t w a l l temperature .

Density of tube-side f l u i d , l b / f t 3 .

Conduct ivi ty of tube-s ide f l u i d , Btu/hr.ft .OF.

S p e c i f i c h e a t of tube-s ide f l u i d , B tu / lb - OF.

\

(CVIS /CVISW) *?kO. 14 .

DIA/CVIS . ~ / C D E N .

(FVIS/FVISW)**0.14 .

QC*CCDEN . Veloc i ty head i n i n n e r window zone.

Veloc i ty head i n cross-f low zone.

Veloc i ty head i n o u t e r window zone.

Net f low a r e a p a r a l l e l t o tubes i n curved-tube r eg ion , f t 2 .

Equiva len t diameter t o be used i n Donohue's c o r r e l a t i o n , f t .

Mass flow r a t e p a r a l l e l t o tubes i n curved-tube r eg ion , l b / h r * f t 2 .

Reynolds number f o r s h e l l - s i d e o f curved-tube reg ion .

P r a n d t l number f o r s h e l l - s i d e of curved-tube reg ion .

Calcu la ted temperature d i f f e r e n c e i n tube-s ide f l u i d between two increments , OF.

Calcu la ted temperature d i f f e r e n c e i n s h e l l - s i d e f l u i d between two increments , OF.

80

ATC 1

F I T

DCURVE PDTO 1

PDSO 1

T 1

T 2

T 1 1

T 1 2

T13

T 24

T 2 5

T 3 6

T 3 7

T3 8

T 4 9

T 4 1 0

TM

BM

ASM

ASM3

ST

S TP

SQ P

S LPR

S LPG

Average temperature i n shel l s i d e of curved-tube r eg ion , OF.

F i n a l number of b a f f l e spaces .

Addi t iona l s t r a i g h t l eng th added t o the curved-tube s e c t i o n , f t .

Tube-side pressure drop i n cunred-tube reg ion , l b / f t 2 .

She l l - s ide p re s su re drop i n curved-tube r eg ion , l b / f t 2 .

Tube-side su r face temperature of tube w a l l , OF.

S h e l l - s i d e su r face temperature of tube w a l l , OF.

Maximum primary (P) s t ress t e s t on ou t s ide s u r f a c e of tube a t bend OD, p s i .

Maximum primary and secondary (P + Q ) stress tes t on ou t s ide s u r f a c e of tube a t bend OD, p s i .

Maximum peak (P + Q + F) stress tes t on o u t s i d e s u r f a c e of tube a t bend OD, p s i .

Maximum primary and secondary (P + Q) stress tes t on o u t s i d e s u r f a c e of tube a t bend I D , p s i . Maximum peak ( P + Q + F) stress t e s t on o u t s i d e s u r f a c e of tube a t bend I D , p s i .

Maximum primary ( P ) s tress t e s t on i n s i d e s u r f a c e o f tube a t bend O D , p s i .

Maximum primary and secondary (P + Q) stress tes t on i n s i d e su r face of tube a t bend OD, p s i .

Maximum peak ( P + Q + F) st ress t e s t on i n s i d e s u r f a c e of tube a t bend OD, p s i .

Maximum primary and secondary ( P + Q) st ress tes t on i n s i d e su r face o f tube a t bend I D , p s i .

Maximum peak ( P f Q + F) s t ress t e s t on i n s i d e s u r f a c e of tube a t bend I D , p s i . Average temperature of tube w a l l a t p o i n t where stresses a r e determined, OF.

Bending moment r e s u l t i n g from r e s t r a i n e d thermal expansion, i n . - l b .

Allowable stress i n t e n s i t y determined i n LAGR, p s i .

Three t i m e s ASM, p s i .

Magnitude of thermal s t ress r e s u l t i n g from DT, p s i .

Hoop s t r e s s r e s u l t i n g from p res su re d i f f e r e n t i a l ac ross tube w a l l , p s i .

Longi tudinal s t ress r e s u l t i n g from P, p s i .

Longi tudinal s t ress r e s u l t i n g from p res su re d i f f e r e n t i a l ac ross tube w a l l , p s i .

Longi tudinal s t ress r e s u l t i n g from p res su re d i f f e r e n t i a l ac ross lower tube s h e e t ( c u r r e n t l y set equal t o z e r o ) , p s i .

81

v s LLO

s LLI

S TTO

STTI

DT

P1 P2

SA

R 1

R2

TL

RB

AA1

AA2

AA3

AA4

AA5

BB 1

BB 2

BB3

BB4

BB5

GFT

A

Magnitude of l ong i tud ina l s t r e s s r e s u l t i n g from BM on o u t s i d e diameter of tube , p s i .

Magnitude of l ong i tud ina l s t r e s s r e s u l t i n g from BM on i n s i d e diameter of tube , p s i .

Magnitude of hoop s t r e s s r e s u l t i n g from BM on ou t s ide diameter of tube, p s i .

Magnitude of hoop stress r e s u l t i n g from BM on i n s i d e diameter of tube , p s i .

Temperature d i f f e r e n t i a l across tube w a l l , OF.

Tube-side p re s su re , p s i .

S h e l l - s i d e pressure , p s i .

Allowable s t r e s s i n t e n s i t y f o r c y c l i c a n a l y s i s , p s i .

I n s i d e r a d i u s of tube, i n .

Outside r ad ius of tube, i n .

Length of tube (d i f f e rence i n e l e v a t i o n of tube ends; HEXLEN i n PRIMEX main program), i n .

Radius of f l e x i b i l i t y bend segments, i n .

Maximum primary (P) stress i n t e n s i t y on ou t s ide su r face of tube a t bend OD, p s i .

Maximum primary and secondary (P + Q ) s t ress i n t e n s i t y on out - s i d e su r face of tube a t bend OD, p s i .

Maximum peak ( P + Q + F) s t r e s s i n t e n s i t y on ou t s ide su r face of tube a t bend OD, p s i .

Maximum primary and secondary (P + Q ) stress i n t e n s i t y on out - s i d e su r face of tube a t bend I D , p s i .

Maximum peak ( P + Q + F) s t r e s s i n t e n s i t y on ou t s ide su r face of tube a t bend I D , p s i .

Maximum primary (P) stress i n t e n s i t y on i n s i d e su r face of tube a t bend OD, p s i .

Maximum primary and secondary (P + Q) s t r e s s i n t e n s i t y on i n s i d e su r face of tube a t bend OD, p s i .

Maximum peak (P + Q + F) stress i n t e n s i t y on i n s i d e su r face of tube a t bend OD, p s i .

Maximum primary and secondary (P + Q ) stress i n t e n s i t y on i n s i d e su r face of tube a t bend I D , p s i .

Maximum peak (P + Q + F) s t r e s s i n t e n s i t y on i n s i d e su r face of tube a t bend I D , p s i .

Conversion f a c t o r , f e e t t o inches.

Arc of four bend segments i n f l e x i b i l i t y bend, r ad ians .

82

DTS

DTT

DP

AMI

EM

PR

TE

SE

DY

RM

Tw

AL

AL2

AK AA P

Average change i n temperature of the s h e l l , O F .

Average change i n temperature of the tubes , OF.

Pressure d i f f e r e n t i a l ac ross tube w a l l , p s i .

Moment of i n e r t i a of tube c ros s s e c t i o n , i n .

Modulus of e l a s t i c i t y f o r tube and s h e l l m a t e r i a l , p s i .

Poisson 's r a t i o f o r tube and s h e l l m a t e r i a l (0.3).

Coef f i c i en t of thermal expansion f o r tube m a t e r i a l , in./in.OF.

Coef f i c i en t of thermal expansion f o r s h e l l m a t e r i a l .

Difference i n thermal expansion of tubes and s h e l l , i n .

Mean r a d i u s of tube w a l l , i n .

Thickness of tube w a l l , i n .

Dimensionless parameter i n Wahl's f a c t o r AK.

Square of AL.

Wahl ' s r i g i d i t y mu1 t i p l i c a t i o n f a c t o r .

Two times A .

Axial load r e s u l t i n g from r e s t r a i n e d thermal expansion, l b .

4

B 1 , B 2 , B 3 , B 4 , B 5 Repeated f a c t o r s used i n c a l c u l a t i n g s t r e s s e s r e s u l t -

s L I Longi tudinal s t r e s s on i n s i d e diameter of tube r e s u l t i n g from

S T I Hoop s t ress on i n s i d e diameter of tube r e s u l t i n g from tempera-

s LO Longi tudinal stress on o u t s i d e diameter of tube r e s u l t i n g from

S TO Hoop s t r e s s on ou t s ide diameter of tube r e s u l t i n g from tempera-

S RPI Radial s t r e s s on i n s i d e diameter of tube r e s u l t i n g from

ing from BM.

temperature d i f f e r e n t i a l across tube w a l l , p s i .

t u r e d i f f e r e n t i a l ac ross tube w a l l , p s i .

temperature d i f f e r e n t i a l ac ross tube w a l l , p s i .

t u r e d i f f e r e n t i a l ac ross tube w a l l , p s i .

p re s su re , p s i .

s u r e , p s i . S RPO Radial s t r e s s on o u t s i d e diameter of tube r e s u l t i n g from pres-

A 1 1 Maximum value of primary (P) stress on o u t s i d e su r face of tube a t bend O D , p s i .

A 1 2 Minimum value of primary ( P ) s t ress on ou t s ide su r face of tube

A13 Maximum value of primary and secondary (P + Q ) s tress on out -

A 1 4 Minimum value of primary and secondary (P + Q ) s t r e s s on out -

a t bend OD, p s i .

s i d e sur face of tube a t bend OD, p s i .

s i d e su r face of tube a t bend OD, p s i .

83

A 1 5

A16

A 2 2

A23

A24

A25

B11

B 1 2

B 13

B 14

B 1 5

B16

B 23

B 24

B 25

B 26

Maximum value of peak ( P + Q + F) stress on o u t s i d e su r face of tube a t bend OD, p s i .

Minimum value of peak ( P + Q + F) stress on ou t s ide su r face of tube a t bend OD, p s i .

Maximum value of primary and secondary ( P + Q) s t r e s s on out- s i d e su r face of tube a t bend I D , p s i .

Minimum value of primary and secondary (P + Q) s t r e s s on ou t - s i d e su r face of tube a t bend I D , p s i .

Maximum value of peak (P + Q + F) stress on ou t s ide su r face of tube a t bend I D , p s i .

Minimum value of peak ( P + Q + F) s t ress on ou t s ide su r face of tube a t bend I D , p s i .

Maximum value of primary (P) s tress on i n s i d e su r face of tube a t bend OD, p s i .

Minimum value of primary (P) stress on i n s i d e su r face of tube a t bend OD, p s i .

Maximum value of primary and secondary ( P + Q) st ress on i n s i d e su r face of tube a t bend OD, p s i .

Minimum value of primary and secondary ( P + Q) s t r e s s on i n s i d e su r face of tube a t bend OD, p s i .

Maximum value of peak (P f Q + F) s t ress on i n s i d e su r face of tube a t bend OD, p s i .

Minimum value of peak ( P + Q + F) s t r e s s on i n s i d e su r face of tube a t bend OD, p s i .

Maximum value of primary and secondary ( P + Q) st ress on i n s i d e su r face of tube a t bend I D , p s i .

Minimum value of primary and secondary (P + Q) s t r e s s on i n s i d e su r face of tube a t bend I D , p s i .

Maximum value of peak (P + Q + F) stress on i n s i d e su r face of tube a t bend I D , p s i .

Minimum value of peak (P + Q + F) stress on i n s i d e sur face of tube a t bend I D , p s i .

Y

Computer Input f o r Reference MSBR Primary Heat Exchanger

I CT M CASM

1 800 00 18OCO.O@ 2 900 . 00 18000 000 3 1ooo.oc 1 7 C 0 3 . 0 0 4 1100.00 13oc0.00 5 1200.00 6CC0.00 6 1300.00 3500.00

HEAT L O A D REQUIRED = 1€!99795808. ( B T L / H R )

ALLOWABLE T O T A L TUBE-SIDE PRESSURE DROP = 1 8 7 2 0 . ( L B / S O - F T )

ALLOWABLE T O T A L S H E L L - S I D E PRESSURE DROP = 16727. ( L B / S O - F T I

TUBE I N L E T PRESSURE = 2 5 9 2 0 ( L B / S Q - F T 1

SHELL OUTLET PRESSURE = 4896. ( L B / S C - F T )

H I G H TEMP. OF S H E L L S I D E F L U I D = 1150.00 ( F 1

H I G H TEMP. OF TUBE S I D E F L U I D = 130C.00 ( F j

LOW TEMP. OF T U B E S I D E F L U I D = 1050.CO ( F I

LOk TEMP. OF S H E L L S I D E F L U I D = 850.0C t F 1

HEAT TRANSFER LEAKAGE FACTOR = 0.8CCOO

PRESSURE LEAKAGE FACTOR = 0.52COO

C O N D U C T I V I T Y O F T U B E WALL METAL = 11.60000 (BTU/HR-FT-F)

ARC OF FOUR BENDS FOR F L E X I B I L I T Y = 60.00 (DEGREES)

INSIDE R A D I U S OF OUTER ANNULUS = 0.83330 ( F E E T )

D I S T A N C E BETWEEN SHELL WALL AND TUBES = 0 . 0 3 1 2 5 ( F E E T )

MAXIMUM A N T I C I P A T E D OUTER R A D I U S OF EXCHANGER = 6.00000 ( F E E T )

NUMBER OF CASES RUN = 1

USE OF ENHANCED TUBES = 1 (ONE I F ENHANCED TUBES ARE USED)

USE OF STRESS A N A L Y S I S SUBROUTINE = 1 (ONE I F TO BE USED)

O U T S I D E DIAMETER OF TUBES = 0 . 0 3 1 2 5 ( F E E T )

WALL T H I C K N E S S OF TUBES = 0 . 0 0 2 9 2 ( F E E T )

R A D I A L P I T C H = 0.06250 ( F E E T )

C I R C U M F E R E N T I A L P I T C H = 0 . 0 6 2 5 0 ( F E E T )

I N N E R B A F F L E CUT3 = 0.40000 ( P E R CENT)

OUTER B A F F L E C U T 4 = 0.400CO ( P E R CENT)

Computer Output f o r Reference MSBR Primary Heat Exchanger

TOTAL HEAT TRANSFEREE = 1 8 9 9 5 6 4 8 0 0 . ( B T U / H R ) (100.9 PERCENT)

MASS FLOW R A T E o f COOLANT = 1 7 5 9 0 7 3 6 . ( L B / H R )

MASS FLOW RATE OF FUEL = 2 3 4 5 4 3 2 0 . ( L B / H R J

S H E F L - S I D E TOTAL PRESSURE DROP = 116.16 (LBISQIN) ( ieo,o P E R C E N T )

T U B E - S I D E TOTAL PRESSURE DROP = 1 2 9 . 6 1 ( L B / S B I N I ( 99.7 FERCENT)

hOMINAL SHELL RADIUS = 2 . 8 3 6 4 ( F T )

UNIFORM BAFFLE S P A C I N G = 0 . 9 3 5 6 ( F T I

TUBE F L U I D VOLUME CONTAINED I N TUBES = 6 7 . 3 8 ( C U B I C F E E T )

TOTAL HEAT TRANSFER AREA B A S E D ON TUBE G.D. = 13037.C2 ( S O F T )

T O T A L NUMBER OF TUBES = 5 8 S 6 .

TOTAL T U e E LENGTH = 2 2 . 5 2 ( F T I

HEAT EXCH, APPROX. LENGTH = 2 1 . 3 1 ( F E E T )

STRAIGHT S E C T I O N OF TUBE LENGTH = 1 8 0 3 5 ( F T )

RADIUS OF THERMAL EXPANSION CURVES = 0 . 8 6 ( F E E T )

B E R G L I N M O D I F I C A T I O N FACTOR = 0 . 8 0

TUBE WALL A V E R A G E TEMP, = 1113.04

SHELL S I D E A V E R A G E TEMP. = 1 0 ~ 7 . 8 3

P S T R E S S A T TUBE O D AND TUBE I D = 673.9C 636.93 (LB /SCIh )

SHOULD NCT E X C E E D 3912,53 I

P+Q S T R E S S AT TUBE OD AND TUBE I D = 11639.02 8317.50 (LB/SCINI

SHOULD NCT E X C E E D 11737.58 J

P+Q+F STRESS AT TUBE O D AND TUBE I D = 13C06.32 10551.26 (LB/SCIN)

SHOULD NGT E X C E E D 25000.00 I

1 TC I T CO CUT T F I TFO FWT TWDT

F F F F F F F

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 1

901150E 0,1129E 0.1115E 0.1101E 0.1087E Oe1074E 0.1060E

0.1032E 0.1046E

0,1018E 0.1004E 0.9895E 0,9754E 0.9614E 0,9474E 0.9334E 0.9194E 0.9054E 0.8915E 0.8776E Co8638E

0 4 0.1129E 04 Co1254E 0 4 0.1115E 04 0o1184E 0 4 Oe1101E C4 001172E 0 4 Oo1087E 04 Co1159E 0 4 0.1074E 04 0.1146E 0 4 0.1Q60E C4 C.1133E 0 4 0,1046E 04 0.1119E 0 4 0.1032E 04 0.1106E 0 4 0.1C18E 04 Ce1093E 0 4 0.1004E 04 0.1080E 0 4 9.9895E @3 0.1067E 0 3 0,9754E 03 0.1054E 0 3 0,9614E 03 Co104CE 0 3 0.9474E 03 0,1027E 0 3 0.9334E 03 0.1014E 0 3 9.9194E 03 0.1001E 0 3 009054E Q3 Ce9874E 03 0.8915E 03 CIeS742E 0 3 0,8776E (33 Co4610E 03 0.8638E c13 0.9479E 03 0.850OE 03 Ce9348E

I v 1 V2 v3 vw1 vw3

F T / S E C

PDSO

LB/SQFT

PDTO

1 2 3 4 5 6 7 8 9

10 11 12 13 1 4 1 5 16 17 18 1 9 20 2 1

0 00 6.1660 6.1475 6.1292 6.1109 6.0927 6.0745 6.0565 6.0384 6.0205 6.0027 5.9849 5.9673 5.9497 5.9323 5.9150 5.8979 5.8808 5.8639 5.8472 5.8306

0.0 - 7.0071 6.9861 6.9653 6.9445 6.9238 6.9032 6.8826 6.8621 6. a418 6.8215 6,8013 6.7812 6.7613 6.7415 6.72 19 6.7024 6. 6830 6. 6638 6.6448 6.6260

0.0 6.7107 6.6905 6.6706 6.6507 6.6309 6.6112 6.5915 6.5719 6.5523 6.5329 6.5136 6.4944 6.4753 6.4564 6.4375 6.4189 6.4003 6.3819 6.3637 6.3457

0.0 6.431 9 6.4126 6. 3935 6.3744 6.3554 6. 3365 6.3176 6.2’388 6.2 a01 6.2615 6.2430 6.2246 6.2063 6.1881 6. 1701 6.1522 6.1344 6.1168 6.0994 6.082 1

O.@ 7.6953 7,6722 7.6493 7.6265 7.6038 7.5812 7.5586 7.5361 7.5137 7.4914 7.4693 7.4473 7.4254 7.4036 7.3821 7. 3606 7.3394 7.3183 7.2974 7.2768

8 5 1 3384 a 51 .3384 8 45 2434 8 39 1812 833.1099 8 27. 0310 8 20 9490 8 14.8638 808.7805 802.6997 796.6255 790.5603 784.5063 778.4670 772.4438 7 66 441 7 7 60 . 4609 754.5051 748.5771 742.6804 736.8167

3430.7144 834.3669 826.6611 8 18 9949 8 11 31 69 803.6326 795 9424 788.2510 780.5627 772.8799 765.2080 757.5488 749.9067 742.2856 734.6880 727.1172 719. 5779 712.0718 704.6025 697.1743 689.7888

I

1 2 3 4 5 6 7 8 9

10 11 12 13 1 4 15 16 17 18 19 20 2 1

RENT0 PRNTO R E N S O l

0.1129E 0 5 0-1090E 0 5 C01059E 0 5 0.1029E 0 5 009998E @ 4 0.9706E 0 4 0.9418E 0 4 0.9134E 0 4 0.8854E C 4 0.8578E 0 4 0.8307E 0 4 0.8041E 0 4 0.7779E 0 4 007523E 0 4 007271E 04 0.7025E 0 4 0.67846 0 4 0.65486 0 4 0.6318E 0 4 0o6094E 0 4 005874E 0 4

0.8172E 01 0.0 008463E 0 1 0.2908E 05 0.8707E 0 1 0.2843E C5 0.8960E 6 1 0.2779E 05 0.9225E 0 1 0.2715E 05 0.9503E 01 0.2651E 05 0.9794E 0 1 0.2587E 05 O e l O l O E 02 0.2523E C5 0.1042E 02 0.2460E C5 0.1075E 02 C.2397E 05 0 . l l l O E 02 0.2335E 05 0.1147E 02 0.2273E 05 0.1186E 02 C02211E 05 0.1226E C2 0.2150E 05 0.1268E 02 0.2089E C5 0.1313E 02 C.2029E 05 0.1360E 02 C.1970E C C 0.1409E 02 0.1912E 05 0.1460E 02 0.1854E 05 0.1514E 02 0.1797E 05 0.1570E 02 0.1740E 05

RENSO2

0.0 0.3304E 05 0.3231E 05 0.3158E 05 0.3085E 05 0.3012E 05 0.2940E 05 0.2868E 05 0.2796E 05 0.2724E 65 0.2653E 05 0.2583E 05 0.2513E 05 0.2443E 05 0.2374E 05 C.2306E 05 0.22396 05 0.2172E 05 0.2107E C5 0.20426 05 0.1978E 05

HTO AHSO UOA HEAT

BTU/HR

RENSC3

BTU / HR/ SOFT/ F

.O

.3164€ 1.3094E ' 3024 E -2954E

0.2958E 04 0.5273E 0 3 0.3980E 03 0.1332E 09 0 5 0.3421E 04 0.2605E 0 4 0.1048E 0 4 0.8775E 08 05 0.3317E 04 0.2552E 0 4 0.1029E C4 0.8748E 08 0 5 0.3244E 04 0.2526E 0 4 0.1018E 0 4 0.87806 08 05 0.3172E 04 0.2500E 0 4 0.1C06E C4 3086C76 08

0.2885E C5 0.3100E 0 4 0.2474E 04 0.9950E 0 3 C.8832E 08 0.2815E 0 5 0.3029E 04 0.2448E 04 0.9833E 03 0.8853E 0 8 0.2746E 05 0.2959E 04 0.2421E 0 4 0.9716E C3 0.8869E 08 0.2677E 05 0.2889E 04 0.2395E 0 4 0.9597E 0 3 0.8882E 08 0.2609E 05 0.2820E 04 0.2368E 0 4 0.9476E 03 0.8890E 08 6.2541E @ 5 0.2751E 04 6.2341E 0 4 0.9355E C3 0.88956 08 0.2473E 0 5 0.2684E 04 0.23146 0 4 0.9233E 0 3 O.8896E 08 0.2496E 05 0.2617E 0 4 0.2287E 0 4 0.9109E C3 0.8892E 08 0.2340E 0 5 0.2551E 04 0.2259E 0 4 0.8985E 03 0.88856 C 8 0.2274E 0 5 0.2485E 04 0.2232E 0 4 0.8860E 0 3 0.88736 08 0.2209E 0 5 0.2421E 04 0.2204E 0 4 0.8733E C3 0.88576 08 0.2144E 0 5 0.2357E 04 0.2177E 0 4 0.8607E C3 0.88316 08 0.20806 0 5 0.2295E 04 0.2149E 0 4 0.8479E 03 0o88136 0 8 @.2018E C5 0.2233E 04 0.2122E 0 4 0.8351E 03 0.8785E 08 0.1955E 05 0.2172E 04 0.2094E 0 4 0.8223E 0 3 0.81526 08 0.1894E 0 5 0.2112E 04 0.2067E 0 4 0.8094E 0 3 0.87166 0 8

90

Appendix C

THE RETEX PROGRAM

The RETEX computer program i s o u t l i n e d i n block-diagram form i n

F ig . C.l. The inpu t da ta requi red f o r t he program a r e given i n Table

C. 1, and the output rece ived from the program a r e given i n Table C. 2 .

A complete l i s t i n g of the main program i s followed by d e f i n i t i o n s of

t he in te rmedia te v a r i a b l e s used i n the program. To i l l u s t r a t e t he use

of the RETEX program, the inpu t and output f o r the MSBR steam r e h e a t e r

exchanger d iscussed i n Subsect ion 3 . 1 of t h i s r e p o r t a r e presented a s

p r i n t e d by the computer.

91

ASSUME BAFFLE SPAC I NG

ASSUME SHELL D I AMETER

CALCULATE NUMBER OF TUBES, FUEL AND COOLANT FLOWS AND VAR I OUS GEOMETR I ES

START WITH F I R S T INCREMENT FROM HOT S I D E OF HEAT EXCHANGER I=1

ASSUME TEMPERATURE DROP FOR THE INCREMENT

EVALUATE ALL PHYSICAL PROPERT I ES AT AVERAGE TEMPERATURE OF INCREMENT

CALCULATE PRESSURE DROPS AND HEAT TRANSFER

CORRELATION FOR DIFFERENT REGIMES COEFF I C I ENTS f O R THE INCREMENT, US I NG CORRECT

CALCULATE HEAT RATE AND TEMPERATURE DROPS OF THE INCREMENT

Fig. C.l. Simplified Flow Diagram of the RETEX Computer Program.

92

CHANGE ASSUMEO

DROP TEMPERATURE DROPS AGREE INCREMENT TEMPERATURE

GO TO NEXT INCREMENT I 1 - 1 END TEMPERATURE OF

CHANGE ASSUMEO SHELL 0 I AMETER

OOES TOTAL TUBE S I D E PRESSURE DROP

CHANGE ASSUMED BAFFLE SPACING

OOES TOTAL SHELL S I D E PRESSURE DROP

6 F i g . C.1 . (continued)

93

ADD I T I ONAL CASES FOR PARAMETER STUDY

P R I N T OUTPUT I

F i g . C . l . (continued)

94

Table C . l . Computer Input Data f o r RETEX Program

Card Columns Format Variab 1 e Term Uni t s

A 1- 10 11-20

2 1- 30

D

1- 10 11-20 21-30 31-40

1- 10

11-20

2 1- 30

1- 10

11-20

21-30

31-35 36-40

El,&, 1-10 ... 11-20 21-30 31-40 41-50

E10.4 F1O.O

F10 .O

F10 .O F10 .O F10 .O F10 .O

F1O.O

F10 .O

F10 .O

F10 .O

F10 .O

F10 .O

I 5 I 5

F10 .O F10 .O F10 .O F10 .O F10 .O

Heat load requi red Allowable tube- s i d e pres -

Allowable s h e l l - s i d e p r e s -

Coolant o u t l e t temperature Fuel i n l e t temperature Fuel o u t l e t temperature Coolant i n l e t temperature

Leakage f a c t o r f o r hea t t r a n s f e r c o r r e l a t i o n s

Leakage f a c t o r f o r pres- s u r e drop c a l c u l a t i o n s

Tube m a t e r i a l conduc t iv i ty

Radius of coolan t c e n t r a l downcomer

Distance between s h e l l wa l l and tube bundle

Maximum a n t i c i p a t e d hea t exchanger r a d i u s

Number of cases t o be run Index one i f enhanced

s u r e drop

s u r e drop

tubes a r e used

Outside diameter of tube Tube wa l l th ickness Tr i angu la r p i t c h Inner b a f f l e c u t Outer b a f f l e c u t

HEATL PRDT

PRDS

CTO FTO ETF ETC

LK

PLK

WCOND

RA5

DTR

RA8MAX

USES KENTB

D I A WTHK TPIP CUT3 CUT4

Btu/hr*f t*OF

f t

f t

f t

f t f t f t % of a rea % of a rea

95

Table C.2. Output Data From RETEX Computer Program

V

T em V a r i a b l e U n i t s

THEATO

HTPERC

QC

QF TTDSO

SPPERC

TTDTU

TPPERC

RA8

BSOI

VOL

AREA

SNT

TUBLEN

GBRL

SAVT

TAVT

T C I ( I )

TCO( I)

CWT ( I )

TFI (I)

TFO( I)

FWT(I)

r n T ( 1 )

V1(1)

v2 (1)

v3 (1)

T o t a l h e a t a c t u a l l y t r a n s f e r r e d

Percentage o f r e q u i r e d h e a t load t r a n s f e r r e d

Coolant ( s h e l l - s i d e ) mass f low r a t e

Fuel ( t u b e - s i d e ) mass flow r a t e

T o t a l t u b e - s i d e p r e s s u r e drop

P e r c e n t a g e of allowed t u b e p r e s s u r e drop

T o t a l s h e l l - s i d e p r e s s u r e drop

Percentage o f allowed s h e l l p r e s s u r e drop

Radius of h e a t exchanger s h e l l

D i s t a n c e between b a f f l e s

F l u i d volume conta ined i n t u b e s

T o t a l h e a t t r a n s f e r a r e a i n h e a t exchanger

T o t a l number o f t u b e s

A c t u a l t u b e l e n g t h

M o d i f i c a t i o n f a c t o r f o r B e r g e l i n ' s h e a t

S h e l l average tempera ture

Tube average tempera ture

Coolant o u t l e t t empera ture from increment 1

Coolant i n l e t t empera ture from increment I

Average t u b e w a l l t empera ture a t c o o l a n t s i d e

F u e l o u t l e t t empera ture from increment I

F u e l i n l e t t empera ture from increment I

Average t u b e w a l l t empera ture a t f u e l s i d e

Average tempera ture drop a c r o s s t u b e w a l l i n

F l u i d average v e l o c i t y i n o u t e r window i n

F l u i d a v e r a g e v e l o c i t y i n o v e r l a p p i n g b a f f l e zone i n increment I

F l u i d average v e l o c i t y i n i n n e r window i n



t r a n s f e r c o r r e l a t i o n

increment I

increment I

increment I

Btu/hr

l b / h r

l b / h r

p s i

p s i

f t

f t

ft3

f t "

f t

O F

O F

O F

"F

OF

O F

OF

OF

OF

f t / s e c

f t / s e c

f t / s e c

96

T a b l e C . 2 (cont inued)

T e r m Var i a b 1 e U n i t s

VWl(I)

vw3 ( 1)

PDSO( I)

PDTO( I)

RENTO( I)

PRNTO ( I)

RENSOl (I)

RENS02 (I)

RENS03 (I) HTO ( I)

AESO( I)

UOA( I)

HEAT (I)

F l u i d v e l o c i t y a c r o s s t u b e s i n o u t e r edge o f

F l u i d v e l o c i t y a c r o s s t u b e s i n i n n e r edge of

S h e l l - s i d e p r e s s u r e drop f o r increment I

Tube-side p r e s s u r e drop f o r increment I

Tube-side Reynolds number f o r increment I

Tube-side P r a n d t l number f o r increment I

Reynolds number i n o u t e r window i n increment I

Reynolds number i n o v e r l a p p i n g b a f f l e zone

Reynolds number i n i n n e r window i n increment I

Tube-side h e a t t r a n s f e r c o e f f i c i e n t i n



i n increment I

increment I

S h e l l - s i d e h e a t t r a n s f e r c o e f f i c i e n t i n increment I

Overall h e a t t r a n s f e r c o e f f i c i e n t i n increment I

Heat t r a n s f e r r e d i n increment I

f t / s e c

f t / s e c

l b / f r? l b / f i?

V

The RETEX Program L i s t i n g

**FTN,Lr E y G r M o QROGPAM MSBRPE-2 MSBPP 10 TYPE REAL LK r L A I J C l 9 LAkC3 MSBRP 29

1 R E N T 0 ( 1 3 O I r P R N T 0 ( 1 3 0 I r P E N S O l ( i 3 0 1 , R E N S O 3 ( 1 ~ 0 ~ T R E N S 0 2 ( 1 3 0 ) 9 MSBRP 3 1 DIMENS I O N TFO( 1301 T C I ( 1 3 0 I r V M l ( 1 3 0 ) ~ V M 2 ( 1 3 0 I r V k l G l ( 1 3 0 I , VW03 (130 1 TMSBRP

VM3 ( 1 3 C I ,PDSO(13O I (NT (100 I r B J ( 3 I r H S O l ( 1 3 O I qHSO2( 130 I r H S O 3 ( 130 I T MSBRP HTC ( 110 I r UOA (1 30 I r TCO ( 1 3 0 I T TF I (1 30 I 9 HEAT ( 1 3 @ I r TkDT ( 130 I r MS BRP

3 0

2 3AHSO( 130 1 4

3 2 3 3

MSBRP 3 L P D T O ( 1 3 0 I r T U B L N ( 1 3 0 I r V I (130 1 , V2( 130 ) t V 3 ( 1 3 0 J r V W 1 ( 130 J 9 V W 3 ( 130) I

5 R (100 I t FPCT( 1 C O I T TCPI (100 I r TCTAL (100 I MSBRP 3 5 6 CWT( I30 I ,FkT ( 1 3 0 I YAVWT ( 1 3 0 I MSBRP 36

1001 FORMAT( € l o o 4 9 2 F 1 0 - GI MSBPP 10 1002 FORMAT( 4 F 1 0 . 0 ) MSBRP 50 1003 FORMAT( 3 F l O e O l MSBRP 60 1004 fOSMAT( 3 F 1 0 - 0 , 2 1 5 1 MSBRP 70 1 0 0 5 FORMAT( 5F10.0) MSBRQ 80 1006 FORMAT(22FOHEAT LOAD REQUIRED = r F 1 2 * O t 2 X r t ? H ( B T U / H R I I MSBRQ 90

1 l O H ( L B / S Q - F T ) I MSBR 101

1 l O H ( L B / S Q - F T I I MSBR 111 1009 FORMAT(33b0PIGF TEMP. CF SHELL S I D E F L U I C = T F I O . ~ T Z X * ~ H ( F I I MSBR 120 1,010 FORMAT(3?HOHIGl’ TEMP. CF TUBE S I D E F L U I C = r F 1 0 0 2 ~ 2 X r 3 H ( F I 1 MSBR 130 1011 FOkMAT(32kOLCk TEMP. CF TUBE S I D E F L U I D = t F 1 0 2 ? 2 X , 3 H ( F I ) MSBR 140 1 0 1 2 FORMAT(32l’OLCW TEMP. OF SHELL S I D E F L U I C = , F I O . Z T Z X , ~ H ( F J I MSBR 1 5 0 1 0 1 3 FORMAT(32kOHEAT TRANSFER LEAKAGE FACTOR = 9F10.5 1 MSBP 160 1014 FORMAT(27kOPRESSURE LEAKAGE FACTOR = , F l O . 5 1 MSBP 170 1 0 1 5 fORMAT(35kOCCNCUCTIVITY OF TUBE WALL METAL = , F 1 0 * 5 ~ 2 X r MSBR 1 8 0

MSBR 1 8 1

1 0 1 7 FORMAT(4ltJOCISTANCE BETWEEN SHELL WALL AND TUBES = MSBR 200 1 r F l O . 5 r 2 X r 6 H ( F E E T I J MSBR 2 0 1

1 0 1 8 FORMAT(49POMAXIMUM ANTICIPATED OUTER RADIUS OF EXCHANGER = 9 MSBR 2 1 0 1 F l o e 5 7 2 X ,6H( FEET I I MSBR 211

1007 FORMAT(43WOALLCWABL€ TCTAL TUBE-SIDE PRESSURE DROP = , F I O . O , Z X r MSBR 100

1 0 0 8 FORMAT(44kOALLCWABLE TCTAL SHELL-SIDE PRESSURE DROP = r F l O e O r 2 X r MSBR 110

1 1 3 H ( BTU/HP-FT-F) J 1016 FORMAT(34kOINSIOE R A C I L S O F CUTEP PNNULQS = r F 1 0 - 5 r 2 X , 6 H ( F E E T ) I MSBR 190

1 0 1 9 FOFMAT(23POhbPeES O F C A S E S RUN = 9 1 4 ) MSBR 2 2 0

1s A R E U S E C ) ) MSBR 2 3 1 1 0 2 1 FORMAT(2GkOCLTZIDE PIAPETER OF TUBES = T F ~ P . ~ ~ ~ X T 6H( FEET) I MSBP 2 4 0 1 0 2 2 FORMAT(27kOkPLL THICKNESS OF TUBES = TFiC. 592x9 6 H ( F E E T l I MSBP 2 5 0 1 0 2 3 FOPMAT(20kGTPIbNGULbR PITCH = 9 ' F ~ O I ~ , ~ X T 6 H ( F E E T ) ) MSBP 260 1 0 2 4 FORMAT(22kOINNER BAFFLE CUT3 = T F L O . 592x9 10H(PEP CENT) I MSBE 2 7 0 1 0 2 5 FCJRMAT(22kOOLTEP BAFFLE CUT4 = r F 1 0 . 5 ~ 2 X ~ 10H(PER CENT) 1 MSBF 2 8 0 1026 FOPMAT(25blTCTAL HEAT TRPNSFEPED = T F ~ ~ . O T ~ X T ~ H ( B T U / H F I T MSBR 2 9 0

1 2 X T l k ( ~ F 5 . 1 y 9 H PERCENT) 1 MSBR 2 9 1 1 0 2 7 FOFMAT(2QkONPSS FLOk RATE OF CCOLANT = , F Z C . O T ~ X , 7H(LB/HRL 1 MSBR 300 1 0 2 8 FO'?MAT(26kOMPSS FLOP' R A T E OF FUEL = TFLO.O,~XT 7 H ( L B / H R I 1 MSBF. 310

1 , 2 X ~ l H ( r F 5 c l r 9 H PERCENT)) MSBR 3 2 1

1 2 X 9 1 b ( T F ~ o ~ T ' H PERCENT) 1 MSBR 331 1 0 3 1 FORMAT(24kChCMINAL SFELL RADIUS = t F 7 , 4 , 2 X ~ 4 H ( F T l I MSBP 340

1 0 3 3 FORMAT(LOF0TUBE F L U I D VOLUME CChTAINEC I h TUBES = 9F7. 2T lXT MSBR 3 6 0 112H(CUBIC FFET I ) MSBR 3 6 1

1 0 3 4 FORMAT(~HCT~EI 'TOTAL HEAT TRANSFER ARE& E A S E D CN TUBE 0.D. = T MSBR 3 7 0 1 F I ~ . ~ T ~ X T ~ H ( S Q F T I 1 MSBR 3 7 1

1 0 1 5 FORMAT(25kOTCTPL NUPBER CF TUBES = vF6oC) MSBR 380 1 0 3 6 FORYAT(21kOTCTAL LEWGTH = T F ~ * ~ T ~ X T ~ H ( F T I I MSBP 3 9 0 1 0 3 7 FORMAT(23k0BWINDOW 1 CROSSFLOW = T F ~ ~ ~ T ~ X ~ ~ H ( S Q F T ) I MSBR 400

MSBR 410

MSBF 4 2 1 MSBR 422

1020 FOSMAT(25kOUSE OF ENHENCEO TUBES = T I ~ T Z X , ? ~ H ( O N E I F ENHENCED TUBEMSBR 2 3 0

1 0 2 9 FORMAT(?4kOSkELL-SIGE TOTAL FRESSUPE D R C P = t F l O o T r 2 X ~ 9H(LB/SQINIMSBF 3 2 0

1 0 3 0 FORMAT(33kOTL'BE-SIDE TCTPL PPESSUR€ D R O P t F 1 0 * 2 9 2 X T 9H(LB/SCINI,MSBR 3 3 0

\o MSBP 350 m 1 0 3 2 FORMAT(26bOUNIFORF BAFFLE SPACING = * F 7 0 4 9 2 X ~ 4 H ( F T ) I

1 0 3 8 FORMAT(31kOBERCLIN VCDTFICATICN FACTOR = 7 F5.2) 1 0 3 9 F O R M A T ( ~ H @ T Z X T ~ H I T ~ X T ~ ~ T C I I S X , ~ H T C ~ , ~ X , ? ~ ~ ~ T T ~ ~ T SHTFI T ~ X T ~ H T F C ! ~ MSBR 420

19x t 3HFWT T E X r4HThDT/ / 1 l x T 1HF T 11 x T ZHF T 11 x T 1HF T 11 X T 2 1 H F ~ 1 1 X t 1HFt ~ ? X T ~ H F T ~ I X T ~ ~ F / / ( ~ X T I ~ T 7E120 4 )

1 0 4 0 FORMAT ( 1 HC T 2X T 1 H I T 7 X T 3EVP? T 9 X T 3HVM2 T 9 X T 3HV P? t 8X t 4HVWO: r 8 X ~ 4 H V k e 3 9

33X t7l 'LB/SQFT// ( 1 x 9 I3 T 7 F 1 2 - 4 I I MSBR 4 3 0 MSBR 4 3 1 1 8 X T ~ H P D S C T 8X T 4HPDf0 / /32 X T 6HFTlSEC

io41 F ~ R M A ? ( ~ ~ C T ~ X T ~ H I , ~ X T ~ H P E N T C ~ ~ X T ~ H P R N T O T ~ X T ~ H R E N S @ Z T ~ X T ~ H R E N S C ~ ~ MSBR 440 16X T 6HF ENSC3 t 7X r3HHTP T 8 X T 4HAHSC! t 9X T 3HUOA 7 8 X t4HHEAT//77X T MSBR 441 Z 13HBTU/FR/SQFT/F 11 3 X t 6 H B T U / H P / / ( l X t I 3 t S E 1 ? - 4 ) I MSBR 4 4 2

1 0 4 3 FOSMAT(ZStOSl-ELL S I D E A V E R A G E TEMP. = 9 F10.21 MSBR 4 6 0 C MSBR 650

1 0 4 2 FORMAT(27kOTURE WALL A V E R A G E TEMP. = ,F10.2) 4 9

C READ I N AhD FRINT OUT INPUT C A T B KEY7= 1 VM 1 ( 1 L =O VM2 ( 1 1 =O VM3 ( 1 I SO. V W O l ( 1 J = O . VW03 (1 J=O R E N S O l ( 1 J =O. R E N S 0 2 ( 1 I = O * RENS03 (1 J = O m

H S O I ( 1 J = O , HS02(1 J = O . HS03(1 J = O ,

C READ 1001, HEATLT PRDTT PRDS READ 1 0 0 2 , CTOT F T O T E T F t ETC REA0 1003~ L K T PLKtWCCND READ 1004, R P 5 9 OTRT R A ~ M A X T K A S E S T K E N T B

READ 1005, C I A 9 WTHK, T R I P , CUT31 CUT4 1 CONTINUE

HSFCT=L. IF(FTOmLT.CTC1 HSFCT=- ls PRINT 1006, PEPTL PRINT 10079 FRCT PRINT 1 0 0 € ~ PRES PRINT 1 0 0 5 ~ C T C PRINT 1010, FTC PRINT 1011, ETF PRINT 1012, ETC PRINT 1013, LK PRINT 10149 PLK P R I N T 1015~ kCCND PRINT 1016, P A 5 PRINT 1017, CTP PRINT 101€, RPEMAX PRINT 1 0 1 5 KPSES PRINT 102C7 K E h T B

MSBR 660 MSBP 490 MSBP 500 MSBR 510 MSBR 520 MSBR 530 MSBR 5 4 0 MSBR 550 MSBR 5 6 0 MSBR 570 MSBR 5 8 0 MSBR 590 MSBR 600 MSBR 83.0 MSBR 6 2 0 MSBR 630 MSBR 640 MSBR 6 5 0 MSBR 660 MSBP 670

MSRR 6 8 0 MSBR 6 9 0 MSBR 700 MSBR 710

MSBR 730 MSBR 740 MSBR 750 MSBR 760 MSBR 770 MSBR 7 8 0 MSBR 790 MSBP 800 MSBR 810 MSBR 820

MSER 720

W W

C C C

2

3

PRINT 1021, CIA PRINT 1022, kTl-K PRINT 1023, TRIP PRINT 1024, CUT3 PRINT 1025, CUT4

BEGIN GEOMETRY CALCULATICNS FOR SINGLE PNNULUS COUNTER FLOW DISC AND COUGHbUT BAFFLEC HEAT EXCH4NGER ATIJBE = (3.14159* (DIA**2.01)/4.0 GFTT = 1./3600. GFT = 1. / 144. DIAI=DIA-f.O*kTHK FATUB =(3.14r59*(DIAI~‘s2.0))/4.0 KEY1 = 0 PE R.Cl = 0.99 IF(KEYl,GT.O~BSOI=O. 5*(@SL+BSHJ KEY2 = 0 PERCZ = 0.99 RASL=RAS RARH=PA8MPX RA8=0. 5* ( RABL +RA8H 1 NT0 = 4~0~~~PP8~~2.0~-~RA5~~2.0~~/~1~12~~T~1P~~2.0~~ RA52=PA5**2 RA82=RA8**2 RA6=(RASZ+CUT4*(RA82-RA521 I**. 5 RAi’=tRA82-CUT3*(RA82-RA521 I**,5 RA62=RA6**2 RA72=RA7**2 AP01=3.1415S*( (RA8J**Z.O-(RA7J**Z.OJ*~l.O-~ATUBE/

1(0,866~((TRIP)4*2,0)))) AP03=3.34159*( (RA6J**Z.O-(RA5J**Z,Ob*tl.C-LATUBE/

l(O. 866*(r( TFIP**2.0) 1) 1 PL4V = O,955*TRIP RB1 = (RPt?-RP7)/(1.86t*TRIPI RB2 = (RP7-RA61/(0.933*TRIPJ RB3 = (RA6-RA5)/(1.86t*TRIpl

MSBR 830 MSBP 840 MSBR 850 MSBR 860 MSBR 870 MSB 1650 MSB 1660 MSB 1670 MSBR 910 MSBR 920 MSBR 930 MSBR 940 MSBR 950 MSBR 960 MSBP 970 MSBF 980 MSBF 990 MSB 1000 MSB 1010 MSB 1020 MSB 1030 MSB 1040 MS8 1050 MSB ?Q60 MSB 1070 MSB 1080 MSB 1090 MSB 1100 MSB 1110 MSB 1111 MSB 1120 MSB 1121 MSB 1130 MSB 1140 MSB 1150 MSB 1160

LAHOl=S. 14155*2,0*FA7*(1.0-~01A/PLAV~ 1 :~~~~=3.1415S*2.O+RA6,(1.0-(DIb/PLIV))

= 4.O~((FA8~~2.C)-(RA7~~2.0~~/(1.12~(TRIP~~2.0~~ SUM1 = ISUMl ISUMZ = 4.0*~~PA7~~2.0~-~PA6~~2.0~~/~1.12~~TR1P~~2.0~~ SUM2 = ISUM ISUM = 4.0~((RA6=~2.CI-(RA5~~2.0~~/(1.12~(TRIP~~2.0~~ SUM3 = ISUM SNT = ISCYl + ISUM + ISUM BSHAX=l,S*t (RAB-(RAE-RA71/2e )-(RA5+(RA6-RA5)/2.1) BStlIN=O. 2*c( RC8-RA5 1 IF(BSHIN.LT,O.~667~BSCIN=0.1667 HU=2.*NCOKD/(DIA*:ALOG(DIA/DIAI~~ 1 CSPHAV=O, 36 FSPHAV=O, 5571 QC=HEATL/ (CSPFAV*( CTO-ETC) I QF=HEATL/ (FSPHAWL FTO-ETF) 1 GTO = QF/ (NTC*FATUB)

4 CONTINUE IFtKEYl. ECwO)BEH=BSMAX IFLKEYl. ECmO1BSL=BSMIN IF(KEYl.EC.O~BSOI=O. 5*(BSL+BSF) IT = 0 KFINAL=O

5 I=1 TSUH=O, SSUM=O. THEATO = C. C TPDTO = 0.0 TPDSO = 090 TFO(I)=FTC TCI(I)=CTC KEY4 = 0 TIF=-5.0 TIC=+.0 CDTF=O, FDTF=O, BSO = BSOI

MSB 1170 MSB 1180 MSB 1190 MSB 1200 MSB 1210 MSB 1220 MSB 1230 YSB 1240 MSB I.250 MSB 1260 MSB 1270 MSB 1280 MSB 1290 MSB 1300 MSB 1310 MSB 1320 MSB 1333 MSB 1340 MSB 1350 Et w MSB 1360 MSB 1370 MSB 1380 MSB 1390 MSB 1400 MSB 1410 MSB 1420 MSB 1430 MSB 1440 MSB 5450 MSB 1460 MSB 1470 MS8 1480 MSB 1490 MSB 1500 MSB 1510 MSB 1520 MSB 1530 MSB 1540

R P L 1 = R Z C / ( ( G P 8 - ( R A 8 - R A 7 ) / 2 . ) - ( R A 5 + ( R b 0 - Q P 5 ) / 2 , ) ) G B R L = 0 . 7 7 * e ~ ~ 1 * * ( - . 1 3 8 ) A W O l = BSC*LAWCl AW03 = BSC*LAWC3 A W 1 = SQPT(PWCl.*APOl I A W 2 = ( A k O l + A k 0 3 ) /2. Ab43 = S Q P T ( P k C 3 * A P @ 3 1 G S 9 1 = Q C / A k l G S O 2 = Q C / A N Z GS03 = Q C / A k ?

6 ATC = T C I ( 1 ) + ( T I C / % . O I CFT = A T C +CCTF*HSFCT ATF = T F G ( I ) + T I F / 2 . FFT=AT F- f CT F*H ZFCT F I = I TUBLN( I I = FI*E!SClI C V I E=O. 2 1 2 1 * E X F ( 4 0 3 2 / ( 4 6 0 . + ATC ) 1 C V I S W = O * 2 1 2 1 * E X P ( 4 0 3 2 . / ( 4 6 9 . + C F T ) 1 CDEN=141. 27-C. C2466*ATC CCON=0.24C C S PH=O 3 6 FV I S=O e06 2 F V I S W = 0.062 FDEN = 0,7632 FCON = 0.036 FSPH = 0.5571 V!SK = ( C V I S / C L I S W l + * O . 1 4 FV I S K = ( F V I S / F V I S W I **O. 14 D C V I S = C I A / C V I S

QCCDEN = C C * C C C E N

R E N T O ( I I = C I A I * C T O / F V I S PRNTO( I) =FVIS*FSPH/FCCh

CCOEN = l./CCEh'

C CALCULATE REYNCLS AND PRANDrL hUMBER TUeE S IDE

H E F I = 1 * + ( ( R E h T C ( I I - 1 O C O - 1/900C. I * * O . 5 I F (KENTB. hE. 1 I k E F I = 1 . PDTO(1 I = ( * 0 0 2 8 + . 2 5 * G E N T O * * ( - a 3 2 ) I * BSC*GTC**?*HEFI/

1 ( C I A I * f C E N * 4 1 7 1 8 2 4 0 0 . I

M S B 1550 M S B 1560 M S B 1570 M S B 1580 M S B 1590 M S B 1600 M S B 1610 MSB 1620 M S B 1630 M S B 1640 M S B 1650

M S B 1670

Y S B 1690 M S B 1700 M S B 1710 M S B 1720 M S B 1730 M S B 1740 MSB 1750

M S B 1770 M S B 1750 M S B 1790 MSB 1800 M S B 1810 M S B 1820 M S B 1830 M S 6 1840 M S B 1850 M S B 2550 M S B 1 8 7 0 M S B 1880 M S B 1890 MSB 1900 M S B 1910 MSB 1911

M S B 1760

C C A L C U L A T E HFPT T R A N S F E R C O E F F T U B E S I D E M S B 2640

GO T O 10 M S B 1940 7 I F ( R E N T O ( I J , L T * 2 1 0 0 . 1 GO T O 9 M S B 1950

1 F V I S K * H E F I * ( l o + , 3333* ( D I A I / T U B L N ( I J J34.6666) M S B 1961 GO TO 10 M S B 1970

9 H T O ( 1 J = F C C N / C I A * ( 4 o 3 6 + ( 0 * 0 2 5 a R E N T O ( I)sPRNTO(I)4DIAI/TUBLN(I I M S B 1 9 8 0 1 ~ / ~ 1 ~ + G ~ 0 0 1 2 * R E N T O ~ I ~ * P R N T O ~ I ~ * D ~ ~ I / T U B L N ~ I I I 1 M S B 1 9 8 1

'10 C O N T I N U E M S B 1990 C C A L C U L A T E F L C W A R E A S S k E L L S I D E M S B 2480

V W g l ( 1 J = Q C C C E N / A W @ l M S B 2010 V W 0 3 ( 1 I = C C C C E N / A W @ 3 M S B 2020 V M l ( I 1 = C S O l * C C D E N M S B 2030 V M 2 ( I I = CSC2*CCDEN M S B 2040 V M 3 ( I J = C S C 3 * C C D E N M S B 2050

C C A L C U L A T E P R E S S U R E D R C P S S H E L L S I D E M S B 2590 D P 1 = ( l o + . @ P @ l I * C D E N * V M l ( I ) * * 2 M S B 2070 DP2 = * 6 * P B 2 * C C E N * V M 2 ( I )**2 M S B 2080 D P 3 = (1. +. 6 * P e 3 ) * C D E N * V M 3 ( I L**2 P S B 2090 R E N S O I ( 1 1 = E S C l * D C V I Z M S B 2 1 0 Q

M S B 2110 R E N S 0 2 ( 1 J = G S C Z * D C V I S M S B 2120 R E N S r 3 3 ( I J = G S C 3 * D C V I S

H E F @ = l . + O . 3 * ( ( P E N S 0 2 ( I J - 1 0 0 0 ~ 1 / 9 0 0 C ~ )**C*5 M S B 2130 I F ( K E N T B o h E o l J ~ E F O = l . M S B 2140 PDSO( I I = ( C F l + D P Z + D P Z ) * P L K * I - E F 0 / 8 3 4 6 2 4 C O O . MSE! 2 1 5 0

C C A L C U L A T E B J F b C T O R ANC S H E L S I D E C O E F F I C I E N T M S @ 273C B J ( 1 ) = ( 0 , " 6 ~ P E N S ~ l ( I J * * ( - O o ~ ~ 2 ) I * G B R L M S B 3170 B J ( 2 1 = ( 0 . 3 L t * R E N S 0 2 ( 1 1 * * ( - 0 . 3 E 2 I ) * G B R L M S B 2 1 8 0 B J ( 3 ) = ( O 0 3 4 C * P E N S O 3 ( I l**(-0*3€21 ) * G B R L M S B 2190 H S O l ( I = ( L K * C S P H * G S C l * @ J ( 1 I*( ( C C C N / ( C S P H * C V I S I 1 4 8 . 6 6 I 1 W I S K M S B 2200 H S 0 2 ( I 1 = ( L K * C S P H * C S C 2 * B J ( 2 I * ( ( C C C N / ( C S P H * C V I S L 66 I l * V I S K M S B 2210 H S 0 3 ( I J = ( L K + C S P H * G S C 3 * B J ( 3 I * ( ( C C C N / ( C S P H * C V I S ) J * * . 6 6 l I * V I S K MSB 2220 A H S ~ ( I I = ( ( ( H S G L ( I ) ~ S U ~ l ) + ( H S C 2 ( I ) ~ S U ~ 2 L + ( H S ~ ~ ( I ) * S U M 3 J J/SNTJ*HEFC M S B 2230 GO TO 12 MSB 2240

11 CONTINUE M S B 2250

H T O ( T ) = F C C N / C I A** 021 7* ( R E N T 0 ( I ) * * a 8 J * ( P R N T C ( I I * ** 2333 1 * F V I S K * H E F I M S B 1930

8 H T O ( I I = F C C n / C I A * , 0 8 9 * ( R E N T O ( I J * * . C 6 6 6 - 1 2 5 * I * ( P R N T O ( 1 ) * * . 3 3 3 3 1 * M S B 1960

+ 0 w

1. 2 UOA(I)=1.C/((1.C)/AHSO(I~~t(1.O/HTO(IJ~t(1.O/HW~~ MS% 2260 A = QFSFSFH MSP 2270 6 = QC*CSFH MS% 2280 0 = UOA( I )+SNT*BSO *3,14159*CIA MS% 2290 P -HSFCT*(C*(A-61 )/(A*%) PBiR = EXP(PI MS% 2310 c = (B-AlsPEAR MS% 2320 TCO(I1 = ((TCI (I )*(B*P@AR-A) I-(TF’2(1 b*P*(PBAR-1. 11 l/C MS% 2330 TFItII =((TCC(I~-TCI(I1~*B/A~ + TFO(II MS% 2340 HEAT1 I I =-A*(TFI(I) - TFO(I)b MS% 2350 TWDT(1) = (HEAT(I~/NTC~*ALOG(DIA/DIAI ~/(2.0*3.14159*BSO*WCONDI MS% 2360 CTIF = TF I( I I-TFO( II MS% 2370 CTIC = TCC(II-TCI(Ib MS% 2380 IF~~ABS~CTIF-TIFI.LE.~1.5~~.ANO.~ABS~CT!C-TIC~.LE.~1.5~~~GO TC 13 MS% 2390 TIF = CTIF MS% 2400 TIC = CTIC MS% 2410 GO TO 6 MS0 2420

13 THEATO = THEATC + HEAT(I) MS% 2430 TPDTO = TFDTC t PDTO(II MS% 2440

zt -P

TP OS0 = TFDSC t PDSOII) MS% 2450 CDTF=(((HEAT(I)I /NTC~/BS0)/(3.14159*DIA*AHSO(I~~ MS% 3090 FDTF=CDTF*AHSG (I 1 /HTO( I! MS% 3100 FWT(I) =PTF-FCTF*HSFCT CWT(I) =ATC+CCTF*HSFCT AVWT( I I =0.5*(FWT(I 1 +CWT(I)) MS% 3130 TSUM=TSUM+AVkT(I) MS% 3140 SSUM=SSUMtATC MS% 2560 IF(KFINAL.EQ.l.AND.I.EQ.ITi GO TO 15 MS% 2460 IF~~~ABS~ETF-TFI~I~1),LE,~~ABS~TFI~I)-TFC~I~~~/2.O~~.OR. MS% 2410

1 (TFI(Ii,LE.ETFI1 Gr- TO 14 MS% 2471 I=Itl MS% 2480 IF ( I.GT. 129 IGG TO 23 MS% 2490 TFO(I1 = lFI(I-11 MS% 2570 TCI(1) = TC@(I-11 MS% 2580 Bso=BsoI MS% 2590 GO TO 6 MS% 2600

14

15

16 17

C

18

19

20

21

KFINAL=l IT=1 FIT = IT GO TO 5 TUBLEN= F IT*RSCI TAVT=TSUM/FIT SAVT=SSUM/FIT CONTINUE VOL = 0.7f!54*(CIAI**2.O~*NTO4TUBLEN CHECK OF TUBE AND SHELL PRESSURE DROPS KEY2 = KEY2 + 1 IF(PERC2.LE.O.11 GO TC 26 IF(TPDT0. LT. (PERC2*PRCTi 1 GO TO 18 IF(TPDTO.GT.PRCTI G@ TC 19 GO TO 20 IF(RA8,LE.(R45 +O- OC51 I GC TO 27 RA8H =RA@ IF(KEY2.NE.30iGO TO 3 RA8L=RABL-0.2 PERC2 = PERC2 - 0.01 KEY2=10 GO TO 3 IF(RA8.GE.(PA8CAX-0.0051 1 GC TC 27 RA8L =RPB IF(KEY2.NE.3CI GO TO 3 RA8H=RA8H+O. 2 PERC2 = PERC2 - 0.01 KEY2=10 GO TO 3 KEY1 = KEY1 t 1 IF(PERCl.LE.O.11 GO TC 25 IF(TPDSO.LT. (PERCl*PRCS) I GO TC 21 IF(TPDSO.ET.PRCSIGO TC 22 GO TO 28 IF(BSOI.LE. (BSb’INtO.OC51 bG0 TC! 24 8SH =BSOI IF(KEYl.NE.3C)CC TO 2

MSB 261’3 MSB 2620 MSB 2630 MS8 2640 MSB 2650

MSB 2680 MSB 2690 MSB 3250 MSB 2710 MSB 2720 MSB 2730 MSB 2740 MSB 2750 MSB 2760 MSB 2770 MS8 2780 MS8 2790 z

b-l MS8 2800 MS8 2810 MSR 2820 MSB 2830 MSB 2840 MSB 2850 MSB 2860 MS6 2870 MS8 2880 MS8 2890 MSB 2900 MSB 2910 MS0 2920 MS6 2930 MS8 2940 MSB 2950 MSB 2960 MSB 2970

BS L=BSL-O. I. MSB 2 9 8 0 MSB 2990 PERCl = P E P C l - 0.01

K E Y l = L O MSB 3000 MSB 3010 GO TO 2 MSB 3 0 2 0

BSL = B S O I MSB 3030 I F ( K E Y l . N E . 3 C I GO TO 2 MSB 3 0 4 0

MSB 3 0 5 0 PERCl = PERCl - 0.01 MSB 3060 KEY1=10 MSf3 3070

MSB 3 0 8 0 GO TO 2 C MSB 3640

MSB 3 6 5 0 C PRINT E X 1 7 S I G h A L S MSB 3110

GO TO 2 8 MSB 3 1 3 0 24 PRINT 1 0 4 5 MSB 3140

MSB 3150

MSB 3 1 7 0 MSB 3 1 8 0

GO TO 28 MSB 3190 MSB 3 2 0 0 2 6 P R I N T 1047

1047 FORMAT(48H l PEPC2 FOR TUBE PRESSURE ORCP I S LESS THEN 0.11 MSB 3 2 1 0 GO TO 2 8 MSB 3 2 2 0

MSB 3230 27 PRINT 1 0 4 E MSB 3 2 4 0 1 0 4 8 FORMAT(29t-1 SHELL R A D I U S = MAX. OR Y 1 N . J

GO TO 2 8 MSB 3 2 5 0 MSB 3 8 1 0 MSB 3 8 2 0 MSB 3 2 8 0 MSB 3290 V l ( I I = V M l ( I J * G F T T MSB 3 3 0 0 V 2 ( I J = VM2( IJ *GFTT

V 3 ( I ) = V M ? ( I ) * G F T T MSB 3310 V W l ( 1 J = V W O l ( I I * G F T T MSB 3 3 2 0 V W 3 ( I J = VWC3(1J*GFTT MSB 3 3 3 0

22 I F ( B S O I * G E . (BSPAX-O.OC5J JGO TO 2 4

BSH=BSH+O,l

2 3 PRINT 1044 ,@SO 1044 FORMAT(39F lEAFFLE SPACINGS EXCEEDE 1 2 9 k I T H BSO = 9 F 5 0 2 9 2 X , 4 H ( F T ) I MSB 3 1 2 0

CL 0

1 0 4 5 FORMAT(ZOk+lBSOT = M A X . OR MIN. J GO TO 28 MSB 3160 m

25 PRINT 1 0 4 6 1046 FORMAT(48I-1 PEPCl FGR SHELL FRESSURE DRCP IS LESS THEN 0.1)

C C END OF C A S E , FPINT CUTPUT

2 8 DO 29 I = 1 , I T

2 9 CONTINUE M S B 3340 TTDSO = TFDSC*CFT M S B 3 3 5 0 TTDTO = TFDTC*GFT M S B 3360 TPPERCzT P CT (341 OC, / PP DT M S B 3370 SPPERC=TPCSO*lCO, / P P OS M S B 3 3 8 0 HTPERC=l OC. *THEATO/HEPTL M S B 3390 AREAz3r 14159*CIA*SNT*TUBLEN M S B 3 4 0 0

C M S B 1640 PR I NT 1 0 2 9 TI-EPTOT HTPEPC M S B '3420 PRINT 1 0 2 7 7 QC M S B 3430 PRINT 1 0 2 e 9 CF M S B 3440 PR I N T 10 2S9 TTDSOT S PP E R C M S B 3 4 5 0 PRINT 103C. TTCTOTTPPERC M S B 3460 PRINT 1 0 3 1 9 R P 8 M S B 3470 PRINT 1 0 3 2 ~ B S O 1 M S B 3 4 8 0 PRINT 10339VCL M S B 3490 PRINT 10347 A R E A M S B 3 5 0 0 PRINT 1 0 3 5 r S N T M S B 3 5 1 0 PRINT 1 0 3 6 r T U B L E N M S B 3 5 2 0 PRINT 103ET G B P L M S B 3 5 3 0 PRINT 1 0 4 2 T T A L T M S B 3 5 4 0 P R I N T 1043 TSAVT M S B 3 5 5 0 PRINT 1 0 3 5 , M S B 3 5 6 0

1 T k C T ( I 1 ) T I = ~ ~ I T I M S B 3 5 6 1

1 I = ~ T I T ) MSB 3 5 7 1

l H T O ( X I t A H S O ( 1 I ,UOA( X I THEAT( I I I t I = l r I T ) M S B 3 5 8 1 M S B 4240 C

C LOOP FOR bDCITIONAL C A S E S I F P E Q U I R E D M S B 4 2 5 0 30 CONTINUE M S B 3610

KEY7=KEY7+1 M S B 3 6 2 0 IF(KEY7.GT.KASESIGO T O 31 M S B 3 6 3 0 GO TO 1 M S B 3 6 4 0

3 1 CONTINUE MSB 3 6 5 0 END M S B 3 6 6 0

+ 0

( I 9 (TC I ( I I ,TCO( I 1 9 CWT ( 1 ) T T F I ( I) TTFO ( I I T FWT( I I 9

PRINT 104c9 ( I 9 ( V I . ( I I 9V2( I ) T V ? ( I I 9vw1( I I 9 V W 3 ( I I ,PCSO( I ) 9PDTO( I I I 9 M S B 3 5 7 0

PRINT 10419 f 1, (RENTO(1 I , PRNTO( 1 ) T F E N S O ~ ( I 1 ,RENSO2(? I ,RENS03( I 1, M S B 3 5 8 0

108

In te rmedia te Variables

The i n t e rmed ia t e v a r i a b l e terms used i n the RETEX computer program

are as def ined f o r the PRIMEX program except for the two terms def ined

below.

TRIP Uniform t r i a n g u l a r p i t c h , f t .

PLAV 0.955WRIP used i n c a l c u l a t i n g the e f f e c t i v e c ross - f low a r e a between the tubes, f t 2 .

Computer Input f o r Reference MSBR Steam Reheater Exchanger

HEAT LOAD REQUIRED * I Z S C C O C C O . (BTU/HR)

ALLOWABLE TOTAL TUBE-SIDE PRESSURE DRCP .I 4120. t L B / S O - F T )

ALLOWABLE TOTAL SHELL-SICE PRESSURE CROP = Ot40. ( L B / S O - F T I

HIGH TEMP. OF SHELL S I D E F L U I C 1150.00 ( F )

HIGH TEMP. OF TUBE S I D E F L U I D .I 1000.00 ( F )

LOU TEMP. OF TUBE S I D E F L U I C 8 650.00 ( F )

LOU TEMP. OF SHELL S I D E F L U I D = eCO.00 ( F I

HEAT TRANSFER LEAKAGE F A C T C R = o.aoooo

PRESSURE LEAKAGE FACTOR = C.5200C

CONDUCTIVITY OF TUBE WALL METAL = 11.6000C (BTL/HR-FT-F 1

I N S I D E RADIUS CF OUTER AhNULUS = c.0 ( F E E T )

DISTANCE BETUEEN SHELL k b L L Ah0 TUBES = 0.04167 ( F E E T )

MAXIMUM ANTICIPATED OUTER RADIUS OF EXCHANGER = 5.CCOOO ( F E E T )

NUMBER OF CASES RUN = 1

USE OF ENHENCED TUBES = 0 (ONE I F ENHENCEC TUBES A R E U S E D )

OUTSIDE DIAMETER OF TUBES = 0.0625C ( F E E T )

WALL THICKNESS OF TUBES = C.00292 ( F E E T )

TRIANGULAR P ITCH = 0.C8331 ( F E E T I

INNER BAFFLE CUT? = C.?OOCO (PEP C E N T )

OUTER BAFFLE CUT4 = C.3OOCO (PER CENT)

Computer Output f o r Reference MSBR Steam Reheater Exchanger

TOTAL HEAT TRANSFERED = 126488992. (BTU/HP I (101.2 PERCENT)

MASS FLOW RATE OF COOLANT = 1157407. ( L B / H R I

MASS FLOW RATE OF FUEL = 641075. ( L B / H R )

SHELL-SIDE TOTAL PRESSURE GPOF = 59.52 ( L B / S O I N ) ( 99.2 PERCENT)

TUBE-SIDE TOTAL PRESSURE DPCP = 29.85 ( L B / S Q I N ) ( 5 9 . 5 PERCENT)

NOMINAL SHELL RADIUS * C . E e 3 E ( F T )

UNIFORM BAFFLE SPACING 0 0.7205 ( F T )

TUBE F L U I D VOLUME CONTAIhEC I h TIJBES * 30.6C ( C U B I C FEET)

TOTAL HEAT TRAhSFER AREA BASEC ON TUeE E.0. 237t.56 (SOFT)

TOTAL NUMBER OF TUBES = 400.

TOTAL TUBE LENGTH ?O.i6 ( F T )

BERGLIN MODIF ICATION FACTOR = 0.75

TUBE WALL AVERIGE TEMF. $ 4 2 . 5 5

SHELL SIDE AVERAGE TEMP. = 1004. 44

1 TC I TCC CUT TF I 1 FO F UT

F F F F F F F

1 2 3 4 5 6 7 8 9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

0.1150E 04 001144E 04 001137E 05 0m1131E 04 O.1124E 04 Oo1118E 04 O o l l l l E 04 0.1104E 04 0.1098E 04 0.1091E 04 001084E 04 Oml077E 04 O.lO7lE 04 001064E 0 4 0.1057E 04 OolO5OE 04 001043E 04 001036E 04 0.1029E 04 0.1022E 0 4 0o1014E 04 0.1007E 04 0m9999E 03 0-9926E 03 0m9853E 03 0.9779E 03 0.9705E 03 009631E 0 3 0.9556E 03 0.9480E 03 009405E 03 009328E 03 0m9252E 03 009175E 03 009098E 03 009020E 03 008942E 03 0m8863E 03 0o8784E 03 0.8705E 03 0m8625E 03 0m8545E 03

0.1144E 04 0.1137E 04 Ool131E 04 0.1124E 04 O.1118E 04 O ~ l l l l E 04 0.1104E C4 0m1098E 04 0.109lE 04 0.1084E 04 0m1077E 04 0.1071E 04 0.1064E 04 0.1057E 04 0,105OE 04 0.1043E 04 0.1036E 04 0.1029E 04 0.1022E 04 0.1014E 04 0.1007E 04 0.9999E 03 0.9926E 03 0.9853E 03 0m9779E 03 0.9705E C3 0.9631E 03

0.9480E 03 0.9405E 03 0.9328E 0 3 0m9252E 03 0.9175E 03 0m9098E 03 0.902OE 03 0.8942E 03 0.8863E 03 0.8784E 03 0.8705E 03 Oo8625E 03 0m8545E 03 0.8464E 03

0.9556E 03

C.1103E C4 001096E 04 C.1089E 04 C.1082E 04 C.1075E C4

C.1061E C4 C.1054E C4 C.1047E C4

C.1032E 04 0-1025E 04 C.1018E 04 C . l O 1 O E 04 Ce1003E 04 C.9956E C3 C.9881E C3 C.9806E C3

C.1068E 04

C.1040E C4

C.9730E 03 C.9654E C3 C09577E 03 C.9500E 03 C.9422E 03 0.9344E C3 C.9265E 03 Cm9186E C3 C.9106E C3

0.8945E C3 C.8864E C3 Co8782E 03 Cm8700E 03 Cm8617E C3 C.8527E 03 C.8444E C3 0.8360E 03 C.8275E 03 C.8190E 03 C.8104E 03 C.8018E 03 Cm7932E 03 0.7845E 03

C.9026E C3

0-5924E 03 009850E 03 0.9775E 03 005699E 03 OmS622E 03 0.5545E 03 0.94e8E 03 0oS390E 03 0.9311E 03 0.9233E 03 005153E C3 0.9073E 03 0.8993E 03 0.8912E 03 0.8831E 03 0.8749E 03 008667E 03 0.8585E 03 0.85ClE 03 0,@418E 03 008334E 03 0.8249E 03 0.8164E 03 Ome079E 03 0.7993E 03 0.7906E 03 0.7819E 03 0.7722E 03 0-7644E 03 0.7555E C3 0.7467E 03 0m7377E 03 0.7287E 03 0.7197E 03 0.7lC6E 03 0.7015E 03 OoC924E 03 0.6831E 03 0.6739E 03 0.6646E 03 O.t552E 03 0.6458E 03

C - 1 O C O E 04 Om5925E 03 OmS850E 03 0.5775E 03 0.5659E 03 O.5622E 03 OoS545E 03 O.5468E 03 Oo5390E 03 O o S 3 1 1 E 03 0.5233E 03 0-5153E 03

0.8993E 03 O.@912E 03 0.8831E 03

O.5073E 03

0.8749E 03 008667E 03 0*85@5E 03 0m85ClE 03 C.8418E 03 0.8334E 03 Oo8249E 03 OeelC4E 03 C.8079E 03 0.79S3E 03 0.79C6E 03 0.7819E 03 0.7732E 03 0m7644E 03 0o7555E 03 C.7467E 03 0.7377E 03 0.7287E 03 0.71C7E 03 C.71C6E 03

Oot924E 03 0.6811E 03

0.7015E 03

0.6739E 03 0.t646E 03 0m6552E 03

0.1090E 04 0.1083E 04 01 1076E 04 0.1069E 04 O.1062E 04 0.1055E 04 001048E 04 0.104lE 04 001033E 04 Oml026E 04 0.1019E 04 0.1012E 04 0m1004E 04 0.9967E 03 0.9892E 03

0o9741E 03 0.9817E 03

0.9665E 03 0.9589E 03 0.95l lE 03 0.9434E 03 0.9356E 03 0.9277E 03 0.9198E 03 0.91 19E 03 0.9039E 03 0.8958E 03 0.8877E 03 0.8795E 03 0.8714E 03 0.8631E 03 0.8548E 03 0m8465E 03 0.8373E 03 0.8289E 03 008204E 03 0.8118E 03 0-8032E 03 0m7946E 03 0.7859E 03 0.7772E 03 0.7684E 03

0.1244E 02 0.1248E 02 0.1255E 02 0.1263E 02 0.1271E 02 O.1279E 02 0m1287E 02 0.1295E 02 0.1302E 02 0o1310E 02 0.1318E 02 0.1326E 02 0.1334E 02 0.1342E 02 0.1350E 02 0.1358E 02 0.3366E 02 0.1374E 02 0.1382E C2 0.13896 02

0.1405E 02 0-1397E 02

0.1413E 02 O.1421E 02 0.1429E 02 0.1437E 02 0.1445E 02 0.1453E 02 0-1461E 02 0.1469E 02 0-1477E 02 0.1485F 02 0.1493E 02 0.1500E 02 0o1508E 02 0.1515E 02 0.1523E 02 Oml531E 02 0.1539E 02 0.1546E 02 0.1554E 02 0m156'1E 02

I V M l VH2 vw3

F T I S E C

vu01 vu03 POSO POTO

L B / S O F f

1 2 3 4 5 6 7 8 9

10 11 12 1 3 1 4 15 16 17 18 19 20 21 22 23 2 4 25 26 27 28 29 30 31 32 33 34 35 3 6 37 38 39 $0 41 42

5.5856 5 .5778 5.570C 5 .5622 5.5543 5 .5465 5 .5385 5 .5306 5. 5226 5. 5147 5.5066 5 .49 a6 5. 4905 5 .4825 5.4744 5 .4662 5 .4581 5 .4495 5 .4417 5 .4335 5.4252 5.4165 5.4086 5. 4003 5 .3920 5.3836 5 .3753 5.3665 5.3585 50 350C 5 .3416 5 .3331 5. 3246 5 .3154 5. 3065 5. 2983 5. 2 8 9 8 5 . 2812 5. 2 7 2 6 5. 264C 5.2554 5 .2468

4 .7e31 4 .7764 4 .7657 4. ' 6 3 0 4. 7 5 6 3 4 .7495

4 . 7 3 t 0 4. 7291 4 .7223 4. 7155 4. 7C86 4. 7 C l 7 4.6547

4 .742e

4. b e t 8 4 .6808 4 .6735 4. 6 6 6 8 4.6 598 4.6528 4. 6457 4. t 3 8 t 4.6115 4. 6244 4. 6173 4. 6 1 0 1 4.6C30 4 .5558 4.5E86 4 .5813 4. 5741 4 .5668 4. 5596 4. 5517 4 .5444 4.5171 4.5297 4. 5224 4. 5150 4 .5c77 4.5C03 4 .4529

6 .4035 6 . 8S38

6 .8745 6 .8648 6 . 8550

6 . 8354 6 . 8256 6 . 8157 6. 8 0 5 8

6 . 7 8 5 9 6. 7759 6 .7659 6 .7559 6 . 7 4 5 8 6 .7357

6 . 7 1 5 4

6 . 6950

6 . 6 7 4 4 6 . 6641 6 . 6 5 3 8

6. 6331 6 .6227 6 . 6123 6 . 6C18 6 . 5914 6. 5809 6 . 5654 6. 5589

6. 5378 6 .5272 6. 5166 6 . 5C60 6 .4953

6.81342

6 . 8453

6 .7959

6 .7255

6 .7052

6. be47

6 ,6435

6. 5484

6 .4847

3.9572 3.9516 3. 9461 3.9406 3.9350 3.9294 3.9238 3.91132 3.9125 3.9C69 3.9012 3.8955 3.8898 3.8841

3.8726 3.8668 3. 8610 3.8552 3.8494 3.8435 3.8377 3.8318 3. 82 59 3.8200 3.8141 3.8C e1 3.8022 3.7962 3.7903 3.7843 3 . 7 7 f 3 3.7723 3.76 57 3.7557 3.7536 3.7476 3.7415 3.7354 3.7293 3.7232 3. 7171

3.8713

6.0447 6 .0362 6 .0278 6 . 0193 6 . 0 1 0 8 6.0023 5.9937 5. 5851 5. S765 5. 5679 5.9592 5. S505 5.541 8 5.5330 5 .9243 5.4155 5. SO66 5.8978 5.8889 5.8800 5.8711 5 .8621 5.8532 5.8442 5. 8351 5 .8261 5 .8170 5 .8C80 5 .7988 5.7897 5.7806 5 .7714 5 .7622 5.7522 5 .7430 5. 7338 50 7245 5. 71 52 5 .7059 5 ,6966 5 .6873 5. 6780

21 0.3354 210 .0414 209.7476 209.4527 209.1567 208.8597 20 8.561 9 208.2632 207.9633 20 7. 6625 20 7. 3607 207.0581 206.7545 206. 4502 2060.1448 205. 8386 20 5. 531 5 20 5. 2235 204- 9145 204.6047 2 0 4 - 2 9 4 2 203. 9826 203.6705 2 0 3 - 3 5 7 6 20 3.043 8 202.7291 20 2.4137 202-0977 201.7808 20 1. 4633 201. 1451 200. 8261 200.5063 200. 1584 1 9 9 - 8 3 7 6 199.5162 19% 1941 1 9 8 - 8 7 1 5 198. 5483 198.2244 19 7.9001 197.5751

102.35 85 102.3585 102.35e5 102.3585 102.3585 102.3585 102.3585 102.3585 102 .35 85 102.3585 102.35 85 102.3555

102.3585

102.3585 102. 35 85 102 .3585 102.35 85 102.35 e5

102.3585 102 . 3585 1 0 2 - 3 5 8 5 102.35 e5 102.35 85 102.3585 102.3585 102 .3585 102.3585 102.3585 102.35 85 102.35 85 102 . 35e5 102 .35 85

1 O?. 33 85 102.3585

102.'3585 102.3585 102.3585

102.35 e5

102.35 e5

io2 .35e5

i o z . 3 5 a 5

102.35 e5

I RENT0 PRNTC R EN S O 1 R ENS02 R ENS03 HT 0 AHSO UOA PEAT

1 0.5794E 06 2 0.5794E O t 3 0.5794E O t 4 005794E 06 5 Oo5794E 06 6 0.5794E O t 7 015794E 06 8 O.5794E O t 9 0,51946 O t

10 005794E O t 11 005794E O t 12 005794E O t 13 0o5794E O t 14 0.5794E O t 15 005794E O t 16 005794E O t 17 005794E 00 18 0.57946 0 6 19 0-5794E O t 20 0.5794E O t 21 005794E O t 22 005794E O t 23 0.5794E O t 24 005794E O t 25 0.5794E O t 26 0.57946 O t 27 0.5794E O t 28 0.5794E O t 29 0.5794E O t 30 0 0 5794E 0.t 3 1 0-5794E O t 32 O.5794E O t 33 0.5794E O t 34 0.5794E O t 35 O05794E O t 36 005794E O t 37 0.5794E O t 30 005794E O t 39 0.5794E O t 40 0-5794E O t 41 005794E O t 42 0.5794E O t

0.9594E 00 0.9594E 00 0.9594E 00 Oe9594E 00 0.9594E 00 0.9594E 90 0.9594E oc 0.9594E 00 0.9594E 00 0.9594E 00 0e9594E 00 0.9594E 00 009594E OC 0.9594E 00 0o9594E 00 0e9594E 00 0.9594E 00 0.9594E OC 0.9594E 00 0.9594E 00 0.9594E 00 0.9594E 00 0.9594E 00 0.9594E OC 0.9594E 00 0e9594E 00 0.9594E 00 0.9594E 00 0.9594E 00 0.9594E 00 0o9594E 00 009594E 00 009594E 00 009594E 00 009594E 00 0.9594E 00 0.9594E 00 0.9594E 00 0.9594E 00 0.9594E 00 0e9594E 00 0.9594E 00

0.5445E 05 Ce5395E 05 C.5340E C5 C.5205E C5 C.5230E 05 C.5175E C5 C.5120E 05 C.5064E 05 C.5008E 05 C.4952E C5 C.4896E C5 G.4835E 05 C04783E C5 C.472tE C5 Ce4669E 05 0.4612E C5 C a 4 5 5 5 E C5 C04497E 05 C.4440E C5 C.4282E C5 C.4324E C5 0.4266E 05 Ca4208E 05 C.4150E 05 C.4092E 05 C04033E C5 C03975E C5 00391tE 05 C.3858E C5 C.3799E 05 Ce3740E 05 Co3682E C5 C.3623E 05 003559E 05 C.3501E C5 C.3442E 05 0.3383E 05 Ce3325E C5 Ce3266E 05 Co3208E C5 0e314SE 05 C.309iE 05

0.4666E 05 0.462OE 05 0.4573E C5 0.4526E 05 0.4479E C5 0-4432E C5 0.4384E C5 0.4336E C5 0.4289E C5 0.4241E 05 0.4152E C5 0.4144E C5 0.40F6E C5 0.4047E 05 0-3998E 05 0.3949E 05 0.3400E C5 0.385lE 05 0.38C2E C5 0.3752E C5 0.3703E C5 0e3653E C5 0.36C3E C5 0.35f4E 05 0.35C4E C5 0e3454E C5 0.34C4E C5 0.3354E C5 0033C3E C5 0e3253E C5 0.3203E C5 0.3153E 05 0.3102E C 5 0.3048E 05 0e2958E 05 0.2947E C5 092897E 05 0.2847E 05 0.2797E 05 0.2747E C5 0.2697E C5 0.2647E C5

Oot735E 05 0.5026E 03 Oet668E 05 0.5026E 03 Cot6COE C5 0.5026E 03 Oet532E 05 0e5026E 03 0 . t464E 05 005026E 03 Oet3S6F C5 0-5026E 03 Oot328E 05 0.5026E 03 Oet259E 0 5 0.5026E 03 C - C l S O E 05 0.5026E 03 006120E 05 0.5026E 03 O.CO51E 05 0.5026E 03 0.5981E 05 0e5026E 03 0.5911E 05 0.5026E 03 0.5841E 05 0.5026E 03 0.5771E 05 0.5026E 03 C.57COE 05 0.5026E 03 0.5629E 05 005026E 03 0.5558E 05 0.5026E 03 0.5487E 05 0.5026E 03 0.5416E 05 0.5026E 03 C.5344E 05 0.5026E 03 0.5273E 05 0.5026E 03 0.5201E 05 0.5026E 03 0.5129E 05 0.5026E 03 0.5057E 05 0.5026E 03 0.4985E C5 0.5026E 03 0e4913E 0 5 0-5026E 03 C.4840E 05 0.5026E 03 0.4768E 05 0.5026E 03 0-46S5E 05 0.5026E 03 004623E 05 0.5026E 03 0.4550E 05 0.5026E 03 094478E 05 0e5026E 03 0.4399E 05 0.5026E 03 0.4326E 05 0.5026E 03 0.4254E 05 0.5026E 03 0 . 4 i e i ~ c5 0 .5026~ 03 C.41C9E 05 0.5026E 03 0.4037E 05 0.5026E 03 0e3964E 05 0.5026E 03 003892E 05 0.5026E 03 013820E 05 0e5026E 03

BTU/HR/SQFT/F

0e1071E 04 0.3137E 03 0.1057E 04 0.3126E 03 0.1054E 04 003123E 0 3 0.1051E 04 0.3120E 03 0.1048E 04 0.3117E 03 0.1044E 04 0-3114E 03 0.1041E 04 0.3111E C3 0.1038E 04 0.3108E 03 0.1034E 04 0.3105E 03 001031E 04 0.3102E 03 0.1027E 04 0.3099E 03 0.1024E 04 0.3096E 03 0.1020E 04 C.3092E 03 001016E 04 0.3089E 02 0.1013E 04 0.3086E 03 0.1009E 04 0.33082E 03 0,1005E C4 0.3079E 03 0.1002E 04 0.3075E 03 009977E G 3 093071E 03 0.9938E 03 0.3068E 03 0.9899E 03 0.3064E 03 0.9859E 03 003060E 03 0.9818E 03 0.3056E 03 0.9777E 03 0.3052E 0 3 0.9736E 03 0.3048E 03 0.9694E 03 0.3044E G3 0.9652E C3 0.3040E 03 0.9609E 03 093036E 03 0-9565E C3 0.3031E 0 3 0-9521E 03 0.3027E 03 0.9476E 03 0e3022E 03 0.9431E 03 0.3018E 03 0.4385E 03 0.3013E 03 0.9335E 03 0.3008E 03 0.9288E 03 C.3003E 03 0.9240E 03 0.2'298E 03 0.9192E 03 0-2493E 03 0.9143E 03 0.2988E 03 0.9094E 03 0.2582E 03 0.9044E 03 0.2577E 03 0.8993E 03 0.2971E 03 0-8942E 03 0.2966E 03

BTU/HP

C.2t73E 07 0 .26e2~ 07 Oo2tS8E 07 0.2715E 07 0.2732E 07 0.2748E 07 0.2765E 07

0.2759E 07

0.2833E 07

0 . 2 7 e 2 ~ 07

0.281tE 07

0.2@50E 07 O.?t?67E 07 0 . 2 a e 4 ~ 07 0925OlE 07 0.2S18F 07 O.ZS35E 07 0.2552E 07 + 0.2969E 07 0125@6E 07

0.3C20E C7

0.3C54E 07

F

0.3CC3E 07

C.?C38E 07

0..3072€ 07 0.3089E 07 0-31C6E C 7 0.2123E 07 0.3140E 07 0 . 3 1 5 7 ~ 07 0.3174E C7 0.319l.E 07 0. 32C8E 07 0.3224E 07 0.3241E 07 0.3257E 07 003274E 0 7 0.3250E 07 0-31C7E 07 0.3323E 07 0.3339E 07 0.335CE 07

114

Appendix D

THE SUPEX PROGRAM

The SUPEX computer program i s o u t l i n e d i n block-diagram form i n

Fig. D . l .

D.l, and the output rece ived from the computer a r e given i n Table D . 2 .

A complete l i s t i n g of the main program and i t s subrou t ines i s followed

by d e f i n i t i o n s of the in te rmedia te v a r i a b l e s used i n the program and the

subrout ines and t h e i r purposes. To i l l u s t r a t e the use of the SUPEX pro-

gram, computer p r i n t - o u t s of the input f o r the MSBR steam genera tor super-

h e a t e r exchanger d iscussed i n Subsect ion 4.1 and the output of t he SUPEX

program a r e presented .

The inpu t da t a requi red f o r the program a r e given i n Table

Y

115

START

READ I N CASE V A R I A B L E S

W R I T E OUT CASE V A R I A B L E S

C A L C U L A T E AVERAGE P H Y S I C A L P R O P E R T I E S FOR T H E O V E R A L L EXCHANGER

C A L C U L A T E G E O M E T R I C PARAMETERS A S S O C I A T E D W I T H T H E B A F F L E WINDOW I +

KNOWING THE ALLOWABLE T O T A L PRESSURE DROP ON THE TUBE S I D E , USE T H E PRESSURE E Q U A T I O N TO C A L C U L A T E A TUBE S I D E MASS F L O I R A T E . C A L C U L A T E A REYNOLDS NUMBER A N 0 FROM T H I S A F R I C T I O N FACTOR. S U B S T I T U T E T H I S F R I C T I O N FACTOR I N T O T H E PRESSURE

ATE TO CONVERGENCE. T H I S G I V E S THE F I R S T GUESS AT TUBE S I D E MASS FLOW RATE.

E Q U A T I O N TO C A t C U L A T E A NEW TUBE S I D E MASS FLOW R A T E ; I T E R -

U S I N G T H E TUBE S I D E MASS FLOW R A T E , E S T I M A T E THE T O T A L NUMBER O F T U B E S IN T H E EXCHANGER.

I 1

r 1 C A L C U L A T E THE G E O M E T R I C FACTORS NECESSARY TO C A L C U L A T E T H E

BERGEL I N FACTORS, THEN C A L C U L A T E THE BERGEL I N FACTORS. 1 I I -

CALCULATE THE TUBE S I D E MASS FLOW RATE FOR AN INTEGER NUMBER OF TUBES. C A L C U L A T E THE G E O M E T R I C PARAMETERS A S S O C I A T E 0 W I T H T H E NUMBER OF R E S T R I C T I O N S I N T H E WINOOW AN0 CROSS FLOW R E G I O N S .

S E T T O T A L PRESSURE DROPS, T O T A L B A F F L E S P A C I N G S A N 0 T O T A L TUBE L E N G T H S TO ZERO.

Fig. D . l . S impl i f ied Flow Diagram of the SUPEX Computer Program.

116

D I V I D E THE T O T A L AMOUNT OF H E A T TO B E TRANSFERRED I N T O EQUAL AMOUNTS FOR EACH INCREMENT.

B A S E D ON T H E T O T A L H E A T TRANSFERRED I N AN INCREMENT, C A L C U L A T E T H E D E L T A - T A N 0 D E L T A - H FOR THE SHELL , S I D E F L U I D FOR ANY INCREMENT.

B E G I N THE INCREMENT C A L C U L A T I O N B Y C A L C U L A T I N G THE TUBE S I D E F L U I D TEMPERATURE AT THE END OF THE INCREMENT.

~

C A L C U L A T E THE LOG-MEAN-DELTA T FOR T H E INCREMENT

C A L C U L A T E THE TUBE WALL RES I STANCE

C A L C U L A T E THE TUBE S I D E F I L M R E S I S T A N C E

C A L C U L A T E THE L E N G T H OF THE INCREMENT

C A L C U L A T E THE TUBE S I D E D E L T A - P FOR T H E INCREMENT

C A L C U L A T E THE ALLOWABLE D E L T A - T ACROSS T H E TUBE WALL B A S E D ON S T R E S S CONS I DERAT I O N S

C A L C U L A T E THE S H E L L S I D E D E L T A - P FOR THE P A R T I C U L A R B A F F L E SPACE

SUM THE TUBE S I D E D E L T A - P ' S

SUM T H E TUBE LENGTHS

e

F i g . D. 1. (cont inued)

117

P ( S D P T ) AND THE ALLOWABLE TUBE S I D E D E L T A - P ( D E L P T A )

ETWEEN THE TOTAL SHELL S I D E D E L T A -

IS W I T H I N 3% OF

ALL OF THE HEAT HAS BEEN TRANSFERRED--THE TOTAL PRESSURE DROPS ON BOTH TUBE AND SHELL S I D E ARE W I T H I N L I M I T S . WE HAVE AN ACCEPTABLE SOLUTION.

W R I T E OUT THE RESULTS.

Fig. D.l. (continued)

118

Table D . l . Computer Input Data f o r SUPEX Program

Card Columns Format Var iab le T e r m Uni t s

1 1- 10 11- 20 2 1- 30 31-40

2 1- 10 11-20 21-30 31-40

3 1- 10 11-20 21-30

31-40

4 1-20 21-40 41-60 61-70

5 1- 10 11-20

21-30

6 1- 10 11-20

21-30

F10.5 F10.5 F10.5 I10

F10.1 F1O.l F10.1 F10.1

F1O.l F1O.l F1O.l

F10.5

E20.6 E20.6 E20.6 F10.5

F10.5 F10.5

F10.5

F10.5 F10.5

F10.5

Tube o u t s i d e diameter Tube w a l l th ickness Tube p i t c h Number of increments

S a l t i n l e t temperature S a l t o u t l e t temperature Steam i n l e t temperature Steam o u t l e t temperature

Steam i n l e t p re s su re Steam e x i t p re s su re Allowable t o t a l s h e l l -

s i d e p re s su re drop Bypass leakage f a c t o r f o r

p re s su re drop

Mass flow r a t e o f steam Mass flow ra te of s a l t To ta l hea t t r a n s f e r r a t e Bypass leakage f a c t o r

S p e c i f i c hea t of s a l t Thermal conduc t iv i ty o f

s a l t (ho t f l u i d ) Estimated number of

b a f f l e spaces

f o r hea t t r a n s f e r

F r a c t i o n a l window c u t Estimated t o t a l tube

Estimated b a f f l e spacing length

DTO THK P N

TH1 TH2 TC 1 TC 2

PC 1 PC2 DELPSA

BLFP

wc WH QT BLFH

CPH TC H

GNB

PW SXG

BSG

in . i n . i n .

OF OF OF OF

p s i p s i p s i

l b /h r l b /h r Btu/hr

B t u / l b OF Btu/f t*hr*OF

f t

f t

W

119

T a b l e D.2. Output Data From SUPEX Computer Program

T e r m Va r i a b 1 e U n i t s

J

IBK( J)

DELTW (J)

DELTWA (J)

TWALL ( J)

DELPS (J)

DHOT (J)

VHOT ( J)

I

X I

TH(I)

TC(I)

PC(1)

DELP ( I)

RI (1)

RW( 1)

RO( 1 )

RT(I)

NLJMT

NBS

B SL

DS

For Each B a f f l e Space

B a f f l e number

Increment number of f i r s t increment which l i e s

C a l c u l a t e d tempera ture drop a c r o s s t u b e w a l l

Allowable tempera ture drop a c r o s s t u b e w a l l based on a l l o w a b l e s t ress

Temperature o f w a l l m a t e r i a l

C a l c u l a t e d s h e l l - s i d e p r e s s u r e drop f o r t h e

Mean d e n s i t y o f h o t f l u i d ( s a l t ) f o r t h e

Mean v i s c o s i t y of h o t f l u i d ( s a l t ) f o r t h e

comple te ly i n b a f f l e space J

b a f f l e space

b a f f l e space

b a f f l e space

For Each Increment

Increment number

Tube l e n g t h f o r t h e increment

Temperature o f h o t f l u i d ( s a l t )

Temperature o f co ld f l u i d (steam)

P r e s s u r e o f co ld f l u i d (steam)

Tube p r e s s u r e drop f o r t h e increment

Thermal resistance o f inside film for the increment

Thermal r e s i s t a n c e o f w a l l m a t e r i a l f o r t h e increment

Thermal r e s i s t a n c e of o u t s i d e f i l m f o r t h e b a f f l e space i n which t h e increment l i e s

c o l d f l u i d s f o r t h e increment T o t a l thermal r e s i s t a n c e between h o t and

For t h e E n t i r e Exchanger

T o t a l number of t u b e s

T o t a l number o f b a f f l e spaces

Length of a b a f f l e space

I n s i d e d iameter of exchanger s h e l l

O F

OF

OF

p s i

lb/ff?

l b / f t * h r

f t

OF

OF

p s i

p s i

hr ' F/Btu

h r OF/Btu

h r * OF/Btu

hr*OF/Btu

f t

i n .

120

Table D.2 (cont inued) ~~

Variab le Un i t s

SDPT To ta l p re s su re drop i n tubes

SDPS To ta l p re s su re drop i n s h e l l

DTLME Log-mean de l t a -T

sx Tota l tube length

p s i

p s i

O F

f t

AREAX T o t a l hea t t r a n s f e r a rea based on t o t a l tube ft?

UEQX Overa l l h e a t t r a n s f e r c o e f f i c i e n t based on Btu /hr*f t" * O F

l ength

t o t a l tube length

SBS T o t a l b a f f l e space length f t

AREAB To ta l hea t t r a n s f e r a r ea based on t o t a l f t 2

UEQB Overa l l hea t t r a n s f e r c o e f f i c i e n t based on Btu/hr*f t" * O F

b a f f l e space length

t o t a l b a f f l e space l eng th

The SUPEX Program Listing

**FTN ,L T G , EvMo PROGRAM SUPEX T Y P E REAL NEW D I M E N S I O N TC( 201 J , TH( 201) ,PC ( 2 0 1 1 (HC (201 J 9

l D E L P S ( 100) ,RW( 201 J (RI ( 201 1 r R O ( l O O 1 ( R T ( 2 0 1 J r U ( 2 0 1 1 9

2X ( 20 1 J 9 DELP ( 201 1 ,DELTWA ( 100 1 ,DELTW( 100 1 , I B K ( 100 1 3DHOT( 50 J ,VHOT( 50 J 9 T k A L L ( 50)

C A L L S V H ( ~ V P V T T V T H J R E A D I N P U T T A P E ~ O ~ ~ O ~ ~ , D T O * T H K T P , N READ INPUTTAP E 5 0 1 1008 9 TH1, TH2 9 TC 1 9 TC2 READINPUTTAPESO, 1OC9,PC 1, PC2 9DELPSA READINPUTTAPE50 , lO lOtWCtWHtQTIBLFH READINPUTTAPESO, 1 0 1 2 r C P P , TCH rGNB READ INPUTTAP E 5 0 , 10 11 D EL P T A=P C 1-PC 2 L O P l = O LOP2=0 LOP3=0 LOP4=0 LOP5=0 L O P 6 = 0 LOP7-0 LOP8=O LOP9=0 LOPlO=O L O P 1 1=0 DELTH=QT/( WH*CPH J DTPB=DELTH/GNB

B L F P

P W SXG T B SG

CALL R I T E l ( DTOeTHK T P t N, T H l r T H 2 9 T C l v T C 2 , PC 1 pPC2 ,DELPTA ,DELPSA, WC, 1 WHt UT ,CPH,TCHTP WVBLFPT B L F H ,GNB,BSG, SXG J

BSL = BSG D T I = ( DTO-Z.O*THK I / 12.0 P = P / 1 2 0 0 DTO=DTO/ l2oO

SUPEX 10 SUPEX 20 SUPEX 30 SUPEX 31 SUPEX 32 SUPEX 33 SUPEX 40 SUPEX 50 SUPEX 60 SUPEX 70 SUPEX 80 SUPEX 90 SUP€ 100 SUP€ 110 SUPE 120 SUPE 130 SUPE 140 SUPE 150 SUP€ 160 SUPE 170 SUPE 180 SUPE 190 SUPE 200 SUPE 210 SUPE 220 SUPE 230 SUP€ 240 SUPE 250 SUPE 2 5 1 SUP€ 260 SUPE 270 SUPE 280 SUPE 290

T C A V = ( T C 1 + T C 2 1 / 2 .O P C A V = ( P C l + P C 2 1 / 2 . 0 C A L L S V H ( 2 r P C l r T C 1 , SPV1,DUMI C A L L S V H ( ~ T P C ~ ~ T C ~ ~ S P V ~ ~ O U M ) C A L L S P V G = ( 2.0* ( S P V l + S P V A V ) + SP V2 I /5.0 CALL C A L L C A L L V I S C O S ( T C A V v P C A V t V I S A V ) V I S G = ( 2.0*( V I S 1 + V I S A V I + V I S2 1 / 5 . @ C FG=O e 0 1 4

S V H ( 2 9 P C A V v TCA V, SP VAV 9 DUM)

V I SCOS ( T C 1, PC 1 9 V I S1 I V I S COS( TC 2 t PC 2 t V I S 2 1

T H E T A L = 0.8 P E R C L = ( T H E T A L - 0 0 5 * S I N F ( 2 . 0 * T H E T A L ) ) / 3 . 1 4 1 5 9 T H E T A U = 1.5707 P E R C U = ( T H E T A U - O . S * S I N F ( 2 .0 *THETAU) I/3.14159

1 NEW = T H E T A L + (PW - P E R C L I * ( T H E T A U - T H E T A L I / ( P E R C U - P E R C L 1 PNEW = (NEW - @ . 5 * S I N F ( 2 o O * N E W ) I /3.14159 E P N E W = A B SF ( P W- PNE W 1 I F ( E P N E W - O . O O l I 4 r 4 ~ 2

2 T H E T A L =NEW P E R C L = PNEW L O P 1 1 = L O P 1 1 + 1 I F ( L O P l l - 1 0 1 1 ~ 1 t 3

3 W R I T E O U T P U T T A P E 5 1 9 1 0 2 2 r L O P l l GOT080

4 T H E T A C = T H E T A L 5 G=3600.O*SQRTF((DELPTA*64.4*144. O * D T I ) / ( C F G * S X G * S P V G ) I

R E G = C T I * G / V I SG

D I F A = A B S F ( C F C - C F G I CFC=(0o00140+(0~125/~REG**Oo321 I ) * 4 o C

I F ( D I F A - O ~ O ~ * C F C I ~ V ~ ~ ~

L O P l = L O P 1+ 1 I F( LOP 1- 10 I 89 8 9 7

6 CFG=CFC

7 W R I T E O U T P U T T A P E 5 1 , 1 0 1 3 r L O P l G O T 0 8 0

S U P E 300 SUPE 310 SUPE 320 SUPE 330 SUPE 340 SUPE 350 SUPE 360 S U P E 370 S U P E 380 SUPE 390 S U P E 400 SUPE 410 SUPE 420 SUPE 430 S U P E 440 S U P E 450 SUPE 460

S U P € 480 N

SUPE 490 SUPE 500 SUPE 510 S U P E 520 SUPE 530 SUPE 540 SUPE 550 SUPE 560 S U P E 570 SUPE 580 SUPE 590 S U P E 600 SUPE 610 SUPE 620 SUPE 630 SUPE 640 SUPE 650

P S U P E 470 N

8

9 1c

11

12

13

14

15

CONTINUE SUPE 660 GOT0 5 SUPE 670 N UMT=X I N TF ( WC*400/ ( G* 3 14 168 D T I **2 1 SUPE 6 8 0 BNUMT=FLOATF(NUMT) SUPE 690 LOPlO=O SUPE 700 DS=P*SQRTf ( 4oO*BNUMT*Oo 866/3 141 6 1 SUPE 710 XBAR = ( D S / 2 * 0 1 * ( T H E T A C - Oo5*S INF(ZoO*THETAC) SUPE 720

B R L l = BSL / (DS-2*C*XBAR) SUPE 730 GBRL = O o 7 7 * B R L l * * ( - O o 1 3 8 ) SUPE 740

SUPE 750 A X = ( 3 14 16*DS**2 /4.0 ) -A k SUPE 760 THETA=( 1050*( 3 1416-( 4. @*AX/DS**Z 1 ) 1 **0.333 SUPE 770 AXC=( 30 1416-THETA+ ( SI NF ( 2 * 0 * T H E T A ) / 2 0) ) * D S * * 2 / 4 * 0 SUPE 780 D I F B = A B S F ( A X C - A X ) SUPE 790 I F ( D I F B - O * 0 2 * A X l I , 5 ~ 1 5 r 1 2 SUPE 800

SUPE 8 1 0

THETA=( AX-AXC 1 *( TH ETA2-THETA 1 / ( A XC2-AXC 1 + THETA SUPE 830 LOPZ=LOP2+1 SUPE 840 I F ( L O P 2 - 1 0 ) 1 4 r 1 4 r 1 3 SUPE 850 WRITEOUTPUTTAPE519 1 0 1 4 9 LOP2 SUPE 860 GOT080 SUPE 8 7 0 CONTINUE SUPE 880 G O T 0 1 1 SUPE 890 GC=4.0*WC/ (BNUMT*3 .1416*DTI * *Z ) SUPE 900

SUPE 910 SUPE 920

XH=( DS/2oO)-XB SUPE 930 CNW= (XH/ (0 R664P ) ) - l o 0 SUPE 940 XC=DS*SINF(THETA) SUPE 9 5 0 PCFB=(P-DTOI /P SUPE 960

SUPE 970 SBK=PCFB*(DS+XC)/Z.O SW=PW*BNUMT*(Oo866*P**Z-( 3 o 1 4 1 6 * 0 T 0 * * 2 / 4 * 0 ) ) SUPE 980 S DPT=Oo 0 SUPE 990 SDPS=O,@ SUP 1000 L O P 8 = 0 SUP 1010

1 -( 2 OS ( S I N F ( THETAC ) * * 3 * 0 1 /3 01 / ( THETAC-0- 5 *S I NF ( 20O*THET AC 1 1 SU PE 721

AW=PW*3o 1416*DS**2 /4 * 0

THETA2=( lo50*(3ol416-(4oO*AXC/DS**2) 1 l * * C 0 3 3 3 AXC2=( 301416-THETA2+( S I N F ( 2 o O*THETA2 1 / 2 * 0 1 I *DS**2 /4oO F

W SUPE 820 N

X B=DS*CO SF ( THETA 1 / 2.@ CNB=2oO*XB/( 0 0 8 6 6 * P )

M S = 1 sx=o SBS=O TC( 1 I = T C 2 TH( 1 ) = T H l R WK= DTO*LOGF( DTO/DT I I / 20 0 PC( 1 )=PC2 C A L L BN=FLOATF(NI QX=QT/BN DECT=QX/ 4 WH*CPH 1 DECH=QX/WC 1 = 1 K = l

L O P 7 = 0

SVH ( 2 r P C 2 r T C 2 r DUM. HC ( 1 I 1

16 SB = SBK*BSL

TCON=TH( I )-DTPB/Zo 0 DENHz141 38E +OC-2 466E-O2*TCON V ISH=O .2 122E+CO*EXPF( 4 0 3 2 .CE+OO/ (TCON+460.OE+00 ) I DHOT(KJ=DENH VHOT ( K 1 = V I SH

GM= W H/ SI3 RECB=CTO*GM/VISH

C O N l = ( CPH*VI SH/TCH I * * O o 6 6 7 E + 0 0

I F(RECB-800.0) 179 1 8 9 1 8 HJB=O 5 7 1/( RECB**@ 4 5 6 ) 17 GOT019 H J 8 = 0 0 3 4 t / ( RECB**@. 3 8 2 I

G W= WH/ SW GS=SQRTF(GM*GW 1 R ECW=DTO*GS/ V I SH

18 19 HB=HJB*CPH*GM/CONl

I F ( R E C W - 8 0 0 . 0 I 2 0 r 2 1 r 2 1 HJW=O 571/ ( R EC W**O 4 5 6 I 2 0 GOT022

2 1 HJW=C!o 34C/ ( R E C W**O 3 8 2 1

SUP 1020 SUP 1030 SUP 1040 SUP 1 0 5 0 SUP 1@60 SUP 1070 SUP 1 0 8 0 SUP 1090 SUP 1100 SUP 1110 SUP 1 1 2 0 SUP 1130 SUP 1140 SUP 1 1 5 0 SUP 1160 SUP 1170 SUP 1 1 8 0 SUP 1190 SUP 1200 SUP 1210 SUP 1 2 2 0 SUP 1230 SUP 1240 SUP 1 2 5 0 SUP 1260 SUP 1270 SUP 1 2 8 0 SUP 1 2 9 0 SUP 1300 SUP 1310 SUP 1 3 2 0 SUP 1330 SUP 1340 SUP 1 3 5 0 SUP 1360 SUP 1370

w

2 2

23

2 4

25

26

27

2 8

29

30 31

32

33

HW=HJW*CPH*GS/CONl SUP 1380 HO=(HB*( l.O-Z,O*PW)tHW*(Z.O*PW) ) * B L F H SUP 1390 HO = HO*GBRL SUP 1400 RO( K ) = l o O/HO SUP 1410 T H ( I + l ) = T H ( I )-DECT SUP 1420 L O P 5 = 0 SUP 1430 HC( I + l ) = H C ( I ) - D E C H SUP 1440 OELP P=Oo 0 SUP 1450 PC( I + l ) = P C ( I )+DELPP SUP 1460 L O P 3 = 0 SUP 1470 L OP 4=0 SUP 1480 T C ( I + l ) = T C ( 1)-DECH SUP 1490 C A L L S V H ( Z t P C ( I+1) t T C ( I+1) tDUMtHCGl SUP 1500 EH=ABSF( HC( 1+1 I-HCG I SUP 1510 I F ( EH-0 00 1* HC 4 I + 1 1 1 3 1 t S 1 7 2 6 SUP 1520 T R I A L = T C ( I + l ) SUP 1530 HRIAL=HCG SUP 1540 TC( I + 1 ) =TC ( I +1) +( HC ( I + 1 I-HCG * ( TC ( I 1 -TC ( I + 1) 1 / ( HC ( 1 CALL$VH( 2,PC( I + l ) t T C ( I+1) (DUMtHCG) SUP 1560 EH=ABSF( HC( I + l ) - H C G I SUP 1570 I F ( E H - O . O O l * H C ( I + l ) ) 3 1 , 3 1 t 2 8 SUP 1580 TNEXT=TC ( I+1) + I HC( I + l ) - H C G ) * (TC ( I+1) - T R I A L ) / (HCG-HRI A L 1 SUP 1590 T R I A L = T C ( I + l ) SUP 1600 HRIAL=HCG SUP 1610 T C ( I + l ) = T N E X T SUP 1620 L OP3=LOP3+1 SUP 1630 I F ( LOP3- 10 1309 30 t 29 SUP 1640 W R I TEOUTPUTTAP E5 1 ,1015, LOP3 SUP 1650 GOT080 SUP 1660 GOT027 SUP 1670 DENOM=(TH( I + l ) - T C ( i t 1 1 ) / ( T H ( I ) - T C ( I 1 ) SUP 1 6 8 C TDEN=ABSF( DENOM-1.0 I SUP 1690 I f ( T DEN-G. 0 5 I 3 2 t 33 9 33 SUP 1700 DELTLM=0.5E+OO*(TH( I + l ) - T C ( I + l ) + T H ( I ) - T C ( I ) I SUP 1710 GO TO 34 SUP 1720 DELTLM=( TH( I + l ) - T C ( I+1 ) -TH( I I +TC (I) 1 /LOGF ( ( T H ( I + l ) - T C ( I + 1 ) I / ( T H ( I )SUP 1730

1-TC ( I 1 I I SUP 1731

F

Ln SUP 1550 r u -HCG 1

34 C O N T I N U E T M = ( T C ( I + l I + T C ( I I ) / 2 . 0 PM=( PC( I + 1 I + P C ( 1 ) I / Z O O

C A L L

C A L L

S V H ( 21 P M T TM I S P V B T H F B )

V I S COS ( TM T P M T V I SB P M = ( P C ( I + l I + P C ( I ) I / 2 . 0

TW=TM+O 2 3 * D E L T L M TCW=0.006375*TW+4.06 RW( I I = R W K / T C W D T F M = O . l * D E L T L M

35 TMS=TM+DTFM C A L L S V H ( ~ T P M T T M S T S P V I T H F I I C A L L C O N D T ( T M S T P M T T C F I 1 C A L L V I SCOS( TMST PM T V I S F 1 ) C R E = ( C T I * G C / V I S F I ) * * 0 . 9 2 3 C P R = ( ( ( H F I - H F B I / ( T M S - T M I ) * ( V I S F I / T C F I 1 I**0.613 C S V = ( SPV B / S P V I I **O . 2 3 1

R I ( I I = D T O / ( H I * D T I ) R T ( I I =RO ( K 1 +RW ( I ) + R I ( I 1 D T F M C = R I ( I ) * D E L T L M / R T ( I 1

H I =O .0@459*( T C F I / D T I I *CRE*CPR*CSV

I F ( A B S F ( DTFM-DTFMC ) - 0 * 0 3 * D T F M C I 3 9 ~ 3 9 ~ 3 6 36 D T F M 2 = ( DTFM+DTFMC I *.5

TMS Z=TM+DTFMZ C A L L C A L L C A L L V I S C O S ( T M S ~ T P M T V I S F I 2 )

S V H ( 2 T PMf TM S 2 T SP V I 2 T H F I 2 I CON DT ( T M S 2 9 PM T TCF I 2 I

C R E 2 = ( D T I * G C / V I S F I 2 ) * * 0 . 9 2 3 C PR 2= ( ( ( HF I 2-H FB I / ( TM S 2-TM I C S V 2 = ( S P V i 3 / S P V I 2 )**0.231 H 2 I =O. 00 4 5 9 * T C F I 2 * C R E 2*CPR2*C SV2 /DT I R 2 I = CTO/ ( H2 I * D T I I R Z T = R O ( K I + R W ( I I + R 2 I DTFMCZ=R 2 I * D E L T L M / R 2 T S L O P E = ( D T F M C - D T F M C Z ) / ( D T F M - D T F M Z I

* ( V I SF I 2 / T C F I 2 I I **O 6 13

D T F M = ( D T F M C - ( S L O P E + D T F M I I / ( l . O - S L O P E I

SUP 1740 S U P 1750 S U P 1760 SUP 1770 SUP 1780 S U P 1 7 9 C SUP 1800 SUP 1810 S U P 1820 SUP 1830 SUP 1840 S U P 1850 SUP 1860 SUP 1870 SUP 1880 S U P 1890 SUP 1900 S U P 1910 S U P 192@ m S U P 1930 S U P 1940 S U P 1950 SUP 1960 SUP 1970 S U P 1980 S U P 1990 S U P 200@ S U P 2010 S U P 2020 SUP 2030 SUP 2040 S U P 2050 SUP 2060 S U P 2070 S U P 2080 SUP 2090

w h,

37

38

39

40

41

42

43 44

4 5

46

47

L O P 4 = L O P 4 + 1 I F ( L O P 4 - 1 0 I 3 8 1 3 8 1 3 7 WRI TEOUTPUTTAPE5 It 10161 L O P 4 G O T 0 8 0 C O N T I N U E G O T 0 3 5 U ( I ) = l o O / R T ( I ) X ( I J=QX/( BNUMT*3o 1 4 1 6 * D T O * U ( I 1 * D E L T L M I R E = D T I * G C / V I S B C F I = O . O 0 1 4 0 + 0 o l 2 5 / ( R E * * ~ o 32) D E L P ( I J = ( 4 o O * C F I * X ( I J / D T I ) * G C * * 2 o O * S P V B / ( 6 4 o 4 ~ 3 6 O O o * ~ 2 . ~ ~ 4 4 o O J D I F C = A B S F ( D E L P ( I J-DELPP J

DELPP=DELP( I ) L O P 5 = L O P 5 + 1

I F ( D I F C - G o 0 5 * D E L P ( I )43943140

I F ( LOP 5- 10 J421 42r 4 1 WRITEOUTPUTTAP E 5 1 1 1 0 1 7 9 L O P 5 G O T 0 8 0 CONTINUE G O T 0 2 4 I F( MS 153 9 531 44 I B K ( K J = I TW= ( R I ( I J+Oo 5*RW ( I 1 1 * ( T H ( I I - TC ( I 4 1 / R T ( I )+ TC ( I ) ALPHA=(OoO031*TW+5o 91) E T W = 3 1 * 6 5-00 00 5*TW CON2=ALPHA*ETk/ ( 1,4*LOGF( D T O / D T I 1 ) CON3=1.0-(2.O*DT0**2*LOGF(DTO/DTI ) / ( D T O * * Z - D T I * * 2 ) ) C O N 3 = C O N 3 * ( - l 0 I I F ( T W - l C l 5 o 3 J 4 5 . 4 6 ~ 4 6 B = 2 4 0 0 0 , 0 S L = 7 0 5 G O T 0 4 7 [email protected] S L = 4 C 0 O CON4=3 0 *( B- SL*T W )-26O(?C C TWALL(KJ=TW D E L T W A i K )=CON4/(CON2*CON3 1 D E L T W ( K I = R W ( I J * c ( T H ( I ) - T C ( I ) ) / R T ( I )

SUP 2100 SUP 2110 SUP 2120 SUP 2130 SUP 2140 SUP 2150 SUP 2160 SUP 2170 SUP 2180 SUP 2190 SUP 2200 SUP 2210 SUP 2220 SUP 2230 SUP 2240 SUP 2250 SUP 2260 SUP 2270 SUP 2 2 8 0 SUP 2290 SUP 2300 SUP 2310 SUP 2320 SUP 2330 SUP 2340 SUP 2 3 5 0 SUP 2360 SUP 2370 SUP 2 3 8 0 SUP 2390 SUP 2400 SUP 2410 SUP 2 4 2 0 SUP 2430 SUP 2440 SUP 2 4 5 0 SUP 2460 SUP 2470

F ru

48 49 50

51 52

53

54

55

56

57

58

59

60

61

62

63

64

IF( I-1151.51.49 IF(N-1)51,51,50 BWN=l.O GOT052 BWN=O. 5 DELPSB=0.6*CNB*(GM/3600.0~**2/~64.4*144.O*DENH~ DELPSW=BWN~~2.0+0.6~CNW~~~GS/[email protected]~~~2/~64.4~144.0~DENH~ DELPS(K)=(DELPSB+DELPSWJ*BLFP SDPS=SDPS+DELPS(K) SBS = SBS+BSL SDPT=SDPT+DELP ( 11 SX=SX+X(IJ IF(N-I162r62.54 I=I+l IF( SBS-SX) 58,5a, 55 MS=0 LOP7=LOP7+1 IF(LOP7-30157,57,56 WRITEOUTPUTTAPE5lr101arLOP7 GOT080 CONTINUE GOT023 MS=1 K=K+l CONTINUE Lopa=Lopa+l IF(LOP8-30)61,61,60 WRITEOUTPUTTAPE51,10l9,LOPa GOT080 CONTINUE GOT016 EDPT=ABSF(SDPT-DELPTAJ IFtEDPT-0.03*DELPTA166,66.63 NUMT=XINTF(BNUMT*(SDPT/DELPTA1**0.35) LOP9=LOP9+1 IF(LOP9-10)65,65,64 WRITEOUTPUTTAPE5lrlO2O,LOP9 GOT0 a0

sup 2480 SUP 2490 SUP 2500 SUP 2510 SUP 2520 SUP 2530 SUP 2540 SUP 2550 SUP 2560 SUP 2570 SUP 2580 SUP 2590 SUP 2600 SUP 2610 SUP 2620 SUP 2630 SUP 2640 SUP 2650 SUP 2660

SUP 2670 SUP 2680 SUP 2690 SUP 2700 SUP 2710 SUP 2720 SUP 2730 SUP 2740 SUP 2750 SUP 2760 SUP 2770 sup 2780 SUP 2790 sup 2800 sup 2810 sup 2820 sup 2830 sup 284c sup 2850

( I . , (

65 CONTINUE SUP 2 8 6 0 BSG=BSL SUP 2 8 7 0 GOT0 10 SUP 2 8 8 0

66 EDPS = ABSF(SDPS - DELPSA) SUP 2 8 9 0 I F ( E D P S - 0*03+DELPSAJ70,70,67 SUP 2 9 0 0

67 BSL = BSL*SQRTF( SDPS/DELPSAJ SUP 2 9 1 0 LOP10=LOP10+1 SUP 2 9 2 0 I F ( LOPIO-10 1 6 9 ~ 6 % 68 SUP 2930

6 8 WRIT EOUT PUTTAP E5 1 T 102 1 T LOP 10 SUP 2940 GOT080 SUP 2 9 5 0

69 CONTINUE SUP 2 9 6 0 GOT015 SUP 2970

70 CONTINUE SUP 2 9 8 0 CALL R I T E 2 SUP 299C J = O SUP 3000

7 1 J N = J + 1 SUP 30 10 JNC=49+J N SUP 3020 I F ( J N . G T * K ) GO TO 7 3 SUP 3030 WRITEOUTPUTTAPE5 1 9 100 1 SUP 3040 a

100 1 FORMAT( l H l , / / ? 3x9 1 H J , 5 X 1 5 H l S T - I 9 ~ X ~ ~ H D E L T - W ~ ~ X ~ ~ H D E L T - W - A T ~ X T SUP 3 0 5 0 1 6HT-WALL T 3x1 6HDELP-St 3x1 6HDENS-H,3 X & H V I SC-H 1 SUP 3 0 5 1

W R I TEOUTPUTTAP E 5 1 1 0 0 2 SUP 3060

NBS = K SUP 3080 DO 7 2 J=JN,K,l SUP 3090 W R I T E O U T P U T T A P E ~ ~ ~ ~ O O ~ , J ~ I B K ( J ~ T D E L T W ~ J ) , D E L T W A ~ J ~ ~ T ~ A L L ~ J ~ ~ SUP 3100

1 OELPS ( J J , DHOT( J J ,VHOT( J 1 SUP 3101 1 0 0 3 FORMAT( 159 3 X * 1 6 ~ 3 x 1 F7.2 ,3X*F 8.2 ~ 2 ( 3 X r F 6 e 1 9 3 X ~ F 6 . 3 J ) SUP 3110

I F ( J . E Q * J N C ) GO TO 7 1 SUP 3 1 2 0 7 2 CONTINUE SUP 3130 73 CONTINUE SUP 3140

CALL R I T E 3 SUP 3 1 5 0 I =c) SUP 3160

74 I N = I + l SUP 3170 I NC =49+ I N SUP 3 1 8 0 I F ( I N * G T . N J GO TO 7 6 SUP 3190 W R I TEOUT PUTTAP E5 1 ,1004 SUP 3 2 0 0

+ N

1002 FORMAT( 1H , 4 ( l H - ) , 3 X , 6 ( 1 H - J r 3 X 1 7 o r 3 X 1 8 ( 1 H - ) , 3 X ~ 8 ( ~ H - ) ~ 4 ( 3 X , 6 ( l H - ) ) ~ / ~ SUP 307@

SUP 3210 SUP 3211

2 4X 9 7HR ES-TOT I SUP 3212 W R I TEOUTPUTTAPE519 l C 0 5 SUP 3220

1005 FORMAT( 1 H ,5(1H-Ir3X16(1H-I13X,2(7(lH-) , 3 X I ~ 8 ( 1 H - ) r 3 X ~ 6 ( 1 H - ) r SUP 3230 1 4( 3 x 9 8 ( 1H- I 1 9 / I SUP 3 2 3 1

DO 7 5 I = I N , N v l SUP 3 2 4 0 SUP 3 2 5 0 RO( I ) = R T ( I I - R I ( I I - R W ( I)

WRITEOUTPUTTAPE519 10069 1, X ( I I 9TH( I ) r T C ( I) . P C ( I I r D E L P ( I I 9 R I ( I I T SUP 3260 1 RW( I I rRO( I J r R T ( I I SUP 3261

1006 F O R M A T ( I ~ ~ ~ X ~ F ~ . ~ T ~ X ~ ~ ( F ~ . ~ , ~ X I t F 8 . 1 9 3 X 9 F 6 . 3 9 4 ( 3 X 9 F 8 . 6 I I SUP 3270 SUP 3280 SUP 3290 7 5 CONTINUE

76 CONTINUE SUP 3300 AREAX= BNUMT* SX*3 . 14 16*DTO SUP 3310 D ENOM=( TH1-TC2 I / ( TH2-TC 1) SUP 3320 TDEN=ABSF( DENOM-1.0 I SUP 3330 I F ( T DEN-0 0 5 1 77 9 7 8 9 7 8 SUP 3340

SUP 3350 GO TO 79 SUP 3360

78 CONTINUE SUP 3370 SUP 3 3 8 0 D T L M E = ( T H L - T C 2 - T H Z + T C l I / L O G F ( ( T H l - T C Z I / ( T H 2 - T C l ) I

79 CONTINUE SUP 3390 SUP 3400 UEQX=QT/ ( AREAX*DTLME I SUP 3410 AREAB=AR EAX*SBS/SX

UEQB=QT/ ( AREABsDTLME 1 SUP 3 4 2 0 DS=DS* lZoO SUP 3430

SUP 3441 SUP 3 4 5 0 8 0 CONTINUE

CALL EX I T SUP 3 4 6 0 1007 FORMAT ( F 10.57 F 10.5 9 F 1 0 * 5 9 I 1 0 1 SUP 3470 1 0 0 8 FORMAT( 4 F 1 0 . 1 ) SUP 3480

1010 FORMAT( E20.69E20.69EZO~C~FlO*5) SUP 3500 SUP 3 5 1 0 SUP 3 5 2 0

1004 FORMAT ( 1H19 / / T 3 x 9 1 H I 9 5X 96HLENGTH 9 4 x 9 5HT-HOTq 5X ~ ~ H T - C O L D I ~ X ~ 1 6HP-CO LD 9 4 X 9 6HDE L P-C 9 4 X 9 6HR ES- I N 9 4 X 9 8HR ES- hAL L 94X T 7 HRES-OUT 9

I F ( 1 o E Q a I N C I GO TO 74

77 DTLME=O* 5E+OC*( THL-TCZ+TH2-TC l )

CALL R I T E 4 ( NUMT, DST SDPTT SCPS ~ D T L M E I S X I A R E A X I U E Q X ~ S B S ~ A R E A B ~ U E Q B ~ SUP 3440 1 N B S v B S L )

1009 FORMAT( F l O ~ l ~ F 1 @ ~ 1 ~ F l O ~ l , F l O o 5 ) SUP 3 4 9 0

1011 FORMAT( 3 F l O o 5 ) 1012 FORMAT( 3 F 1 0 . 5 )

1013 FORMAT(8H LOP 1 = I 4 1 1014 FORMAT(8H LOP 2 =I41 1 0 1 5 FORMAT(8H LOP 3 =I41 1016 FORMAT(8H LOP 4 = I 4 ) 1017 FORMAT(8H LOP 5 =I41 1 0 1 8 FORMAT(8H LOP 7 =I41 1019 FORMAT(8H LOP 8 =I4J 1020 FORMAT(8H LOP 9 =I41 1021 FORMAT(9H LOP 10 =I41 1022 FORMAT(9H LOP 11 = I 4 1

END

SUBROUT I N E RITE1(DTO,THK, P T N vTH11TH2 r T C l , T C 2 t P C l rPC29 DELPTA, 1 DELPSAt WC 9 WHp QT TCPH, TCHIP W 96L FP, B L F H rGNB 9 BSG SXG J

W R I TEOUTPUTTAP E 5 1 * 1 0 0 1 WRITEOUTPUTTAP E519 1C02, D T C WRITEOUTPUTTAPE519 1003, THK W R I TEOUTPUTTAP E 5 1 9 1004 9 P W R I T EOUT PUTTAP E5 1,109 5 9 N WR I TEOUTPUTT AP E 5 1 , 1006 9 TH 1 WRITEOUTPUTTAPE51, 1 0 0 7 9 T H 2 WRITEOUTPUTTAPE51 ,1 ! l@8,TCl W R I TEOUTPUTTAP E5 1 ,1009, TC 2 WRI TEOUTPUTTAP E 5 1,1010 , PC2 W RX TEOUTPUTTAP E5 1, 1 0 1 1, DE LPTA WRI TEOUTPUTTAP E5 1,1012 9 DELPSA WRITEOUTPUTTAPE5 l r le139 WC WRITEOUTPUTTAPE51,1014,hH W R I T E O U T P U T T A P E 5 1 , 1 0 1 5 r Q T WR I TEOUTPUTTAP E5 1 , 1 0 1 6 9 CPH WRI TEOUTPUTTAP E5 1 9 10179 TCH W R I TEOUTPUTTAP E5 1 ,1018 , PW WRITEOUTPUTTAPE51,1019, BLFP

SUP 3 5 3 0 SUP 3540 SUP 3 5 5 0 SUP 3560 SUP 3 5 7 0 SUP 3 5 8 0 SUP 3 5 9 0 SUP 3600 SUP 3610 SUP 3620 SUP 3630

R I T E l 10 R I T E l 11 w R I T E l 20 R I T E l 30 R I T E l 40 R I T E l 50 R I T E l 60 R I T E 1 70 R I T E l 80 R I T E l 90 R I T E 100 R I T E 110 R I T E 12C R I T E 130 R I T E 140 R I T E 150 R I T E 160 R I T E 17@ R I T E 180 R I T E 190 R I T E 200

w

w

WRITEOUTPUTTAPE5 l r 1 0 2 0 r B L F H R I T E 210 R I T E 220 NBSR = I F I X ( G N B )

W R I TEOUTPUTTAP E5 1 ,102 1 9 NB SR R I T E 230 W R I T E O U T P U T T A P E 5 l r l C 2 2 r B S G R I T E 240 WRITEOUTPUTTAPE51,1O23, S X G R I T E 2 5 0 RETURN R I T E 260

R I T E 2 7 1 1002 FORMAT( 1 H r 3 6 H O U T S I D E DIAMETER OF TUBES ( I N C H E S ) = rF6 .3 ) R I T E 280

R I T E 2 9 0 1004 FORMAT( l H O r 2 1 H T U B E P I T C H ( I N C H E S ) = rF7.4) R I T E 300

l I D E D = ~ 1 4 r / / ) R I T E 311 1006 FORMAT( 1 H 0 , 3 t H I N L E T TEMPERATURE OF HCT F L U I D ( F ) = r F 7 . 1 ) R I T E 3 2 0

R I T E 330 R I T E 340

1009 FORMAT( 1HOr38HOUTLET TEMPERATURE OF COLD F L U I D ( F ) = , F 7 o l ~ / / ) R I T E 3 5 0 1010 FORMAT( lHO,37HOUTLET PRESSURE OF COLD F L U I D ( P S I ) = vF7.1) R I T E 360

1 F7.1) R I T E 3 7 1

1 F 7 . 1 ~ / / ) R I T E 3 8 1 1013 FORMAT( lhOv38HMASS FLOW RATE OF CCLD F L U I D ( L B / H R ) = r l P E 1 0 . 3 ) R I T E 390

R I T E 400 1015 FORMAT( l H O v 3 5 H T O T A L HEAT TRANSFER RATE ( B T U / H R ) = r l P E 1 0 . 3 ) R I T E 410

R I T E 420

R I T E 4 3 1 1018 FORMAT( l H O r 2 3 H F R A C T I O N A L kINDOW CUT= r F 5 + 2 r / / ) R I T E 440 1019 FORMAT( l H O r 3 7 H B Y - P A S S LEAKAGE FACTOR FOR PRESSURE= r F 6 . 3 ) R I T E 450

1001 FORMAT( l H 1 , / / , 2 4 X , 6 9 H * * * THE FOLLOWING I S THE INPUT I N F O R M A T I O N R I T E 2 7 0 1 FOR T H I S PROBLEM * * * , / / / I

1003 FORMAT( l H 0 9 3 0 H T U B E WALL THICKNESS ( I N C H E S ) = ~ F 7 . 4 )

1 0 9 5 FORMAT( lH0v58HNUMBER OF INCREMENTS I N T O WHICH THE EXCHANGER I S D I V R I T E 310

1007 FORMAT( l H O r 3 7 H O U T L E T TEMPERATURE OF HOT F L U I D ( F ) = 1F7.1) 1008 FORMAT( 1 H O r 3 7 H I N L E T TEMPERATURE OF CCLD F L U I D ( F ) = r F 7 . 1 )

w w

1011 F O R M A T ( l H O r 5 0 H A L L O k A B L E TOTAL PRESSURE DROP CN TUBE S I D E ( P S I ) = 9 R I T E 370 10

1012 FORMAT( lHO,51HALLOkABLE TCTAL PRESSURE DRCP CN SHELL S I O E ( P S I ) = r R I T E 380

1014 FORMAT( ~ H O T ~ ~ H M A S S FLOW RATE OF HOT F L U I D ( L B / H R ) = r l P E 1 0 . 3 )

1016 FORMAT( l H O r 3 9 H S P E C I F I C FEAT OF HCT F L U I D (BTU/LE-F)= r F 6 . 3 ) 1017 FORMAT( lHOr49HTHERMAL C O N D U C T I V I T Y OF HOT F L U I D (BTU/HR-FT-F)= 9 R I T E 43@

1 F6.3)

1020 FORMAT( ~ H O I ~ ~ H ~ Y - P A S S LEAKAGE FACTOR FOR HEAT TRANSFER= , F 6 . 3 r / / ) R I T E 460 1 0 2 1 FORMAT( lHO,50HESTIMATE OF THE NUMBER OF BAFFLE SPACES REQUIRED= T R I T E 470

1 0 2 2 FORMAT( lH0 ,46HESTIMATE OF THE LENGTH OF A BAFFLE S P A C E ( F T I = r F 5 . 2 ) R I T E 4 8 0 1 0 2 3 FORMAT( L H O T ~ ~ H E S T I M A T E OF THE TOTAL TUBE LENGTH(FT)= r F 6 . 2 )

1 1 3 ) R I T E 471

R I T E 490 END R I T E 500

e

SUBROUTINE R I T E 2 R I T E 2 10 W R I TEOUTPUTTAP E5 1 r 1001 R I T E 2 20 W R I TEOUTPUTTAP E 5 1 r 1 0 0 2 R I T E 2 30 W R I TEOUTPUTTAP E5 1 T 1 0 0 3 R I T E 2 40 WRI TEOUTPUTTAP E 5 1 9 1 0 0 4 R I T E 2 5C W R I T E O U T P U T T A P E 5 1 r l 0 0 5 R I T E 2 60 W R I TEOUTPUTTAP E5 191006 R I T E 2 70 WRI TEOUTPUTTAP E 5 1 T 1@07 R I T E 2 80 WRI TEOUTPUTTAP E5 1 T 1 0 0 8 R I T E 2 90 WRI TEOUTPUTTAPESl r 1009 R I T E 100 RETURN R I T E 110

1001 F O R M A T ( ~ H L T / / T ~ ~ X T ~ ~ H * * * THE FOLLOWING TABLE GIVES INFORMATION R I T E 120 l F O R EACH BAFFLE SPACE THROUGH THE EXCHANGER * * * t / / r 3 5 X r 5 O H T H E C R I T E 121 20LUMN LABELS FOR T H I S TABLE ARE D E F I K E D B E L O h r / / / / ) R I T E 122

1002 FORMAT( l H O r 3 O H J BAFFLE SPACE NUMBER) R I T E 130 1003 FORMAT( l H O r 8 6 H l S T - I INCREMENT NUMBER OF F I R S T INCREMENT W H I C H R I T E 140

1 L I E S COMPLETELY I N BAFFLE SPACE J) R I T E 141 1004 FORMAT( lHO959HDELT-W CALCULATED TEMPERATURE CROP ACROSS TUBE WRITE 1 5 0

lALL ( F f ) R I T E 1 5 1 w

1LL BASED ON ALLOWABLE STRESS ( F ) 1 R I T E 161 1006 FORMAT( lHOp40HT-WALL kALL M A T E R I A L TEMPERATURE ( F ) 1 R I T E 170 1007 FORMAT( 1 H O r 08HDELP-S CALCULATED SHELL PRESSURE DROP FOR THE B A R I T E 1 8 0

l F F L E SPACE ( P S I ) ) R I T E 1 8 1 1 0 0 8 FORMAT( lKOr7CHDENS-H MEAN D E N S I T Y OF THE HCT F L U I D FOR THE B P F R I T E 190

l F L E SPACE ( L B / F T 3 ) 1 R I T E 191 1009 FORMAT( l H O 9 7 4 H V I S C - H MEAN V I S C O S I T Y OF THE HCT F L U I D FOR THE B R I T E 200

l A F F L E SPACE ( L B / F T - H R I 1 R I T E 201 END R I T E 210

w w

1 0 0 5 FORMAT( 1 H O v 84HDELT-W-A ALLOWABLE TEMPERATURE D R O P ACROSS TUBE WARITE 160

SUBROUTINE R I T E 3 R I T E 3 10 WR I TEOUTPUTTAP E 5 1 9 1 O@ 1 R I T E 3 20 WRI TEOUTPUTTAP E5 l q l C ’ 0 2 R I T E 3 30 WR I TEOUTPUTTAP E5 I q 1 C03 R I T E 3 40 W R I TEOUTPUTTAP E5 191004 R I T E 3 50 WRI TEOUTPUTTAPE51q1005 R I T E 3 60 WRI TEOUTPUTTAP E519 1 0 0 6 R I T E 3 70 WRITEOUTPUTTAPE519 10C7 R I T E 3 80 W R I TEOUTPUTTAPE5 1 9 1008 R I T E 3 90 W R I TEOUTPUTTAP E 5 1 9 1009 R I T E 100 W R I TEOUT PUTTAP E5 1 9 10 10 R I T E 110 WRITEOUTPUTTAPE5 l r 1011 R I T E 120 RETURN R I T E 130

1001 FORMAT( l H l , / / r 1 4 X , 9 1 H * * * THE FOLLOWING TABLE GIVES INFORMATION R I T E 140 1AT EACH INCREMENT THROUGH THE EXCHANGER * * * r / / v 3 5 X 9 5 0 H T H E COLUMRITE 141 2N LABELS FOR T H I S TABLE ARE DEFINED B E L C k r / / / / ) R I T E 142

1 0 0 2 FORMAT( 1 H 0 9 2 7 H I INCREMENT NUMBER) R I T E 150 1 0 0 3 FORMAT( lHOv47HLENGTH TUBE LENGTH FOR THE INCREHENT ( F E E T ) ) R I T E 160 1004 FORMAT( l H 0 9 4 3 H T - H O T TEMPERATURE OF THE HOT F L U I D ( F ) ) R I T E 170 F. 1005 FORMAT( lH0,44HT-COLD TEMPERATURE OF THE CCLD F L U I D ( F I ) R I T E 180 100 6 FORMAT ( 1 k0 9 4 3HP-CO L D PRESSURE OF THE CCLD F L U I D ( P S I I I R I T E 190 1007 FORMAT( lHO953HDELP-C TUBE PRESSURE DROP FOR THE INCREMENT ( P S I R I T E 200

1) 1 R I T E 2 0 1 1 0 0 8 FORMAT ( 1HO 9 77HRES- I N THERMAL RESISTANCE OF THE I N S I D E F I L M FGRRITE 210

1 THE INCREMENT (HR-F /BTU) ) R I T E 211

1 0 R THE INCREMENT (HR-F /BTU) ) R I T E 221 1010 FORMAT( lHQv109HRES-OUT THERMAL RESISTANCE OF THE OUTSIDE F I L M F R I T E 230

1 0 R THE BAFFLE SPACE I N h H I C H THE INCREMENT L I E S ( H R - F / B T U ) ) R I T E 2 3 1 l C l l FORMAT( lH9990HRES-TOT TOTAL THERMAL REZISTANCE BETWEEN HOT E CORITE 240

R I T E 241 1LD F L U I D S FOR THE INCREMENT ( H R - F I B T U ) ) END R I T E 250

P w

1 0 3 9 FORMAT( lHOt79HRES-WALL THERMAL RESISTANCE OF THE WALL MATERIAL F R I T E 2 2 0

. ' (

SUBROUT I NE R I T E 4 ( NUMT 9 DST SDP T 9 SDPS ,DTLME T SX AREAX (UEQX t S b S 9 R I T E 4 10 1 A R E A B T U E Q B T N B S T B S L ~ R I T E 4 11

WRITEOUTPUTTAPE519 1001 R I T E 4 20 W R I TEOUTPUTTAP E 5 1 1 10@29 NUMT R I T E 4 30 W R I TEOUTPUTTAPE51,1003 9 NB S R I T E 4 40 W R I TEOUTPUTTAP E5 IT 10049 B S L R I T E 4 50 WRI TEOUT PUTTAP E 5 1 9 1 0 0 5 9 OS R I T E 4 60 W R I TEOUTPUTTAP E519 1 0 0 6 9 SDPT R I T E 4 70 W R I TEOUTPUTTAP E5 1 9 1 0 0 7 9 SDPS R I T E 4 80

R I T E 4 90 W R I TEOUTPUTTAP E5 1 9 10099 SX R I T E 100

R I T E 110 W R I TEOUTPUTTAP E 5 1 9 1011 9 UEQX R I T E 120 WRI TEOUTPUTTAP E 5 1 1 1 0 1 2 ~ SB S R I T E 130 WRI TEOUTPUTTAP E5 1 9 1 O 1 3 9 AREAB R I T E 140 WRI TEOUTPUTTAP E5 1910149 UEQB R I T E 150 RETURN R I T E 160

WRITEOUTPUTTAPE5 l r 1 0 0 8 r O T L M E

W R I T EOUT PUTTAP E5 1 9 1 0 10 AR EA X

F W

1001 F O R M A T ( ~ H L ~ / / , ~ ~ X T ~ ~ H * 4 * THE FOLLCWING ARE AVERAGE OR TOTAL PRORITE 170 l P E R T I E S FOR THE ENTIRE EXCHANGER * * * * / / I R I T E 171 ul

1002 FORMAT( lH0,23HTOTAL NUMBER OF TUBES= , 1 5 1 R I T E 180 1003 FORMAT( l H 0 9 3 1 H T O T A L NUMBER OF BAFFLE SPACES= 9 1 4 1 R I T E 190 1004 FORMAT( lH0932HLENGTH OF A BAFFLE S P A C I N G ( F T I = r F 6 . 3 ) R I T E 200

1006 FORMAT( lHO936HTOTAL PRESSURE DROP I N TUBES ( P S I ) = ~ F 8 . 2 ) R I T E 220 1007 FORMAT( lHO936HTOTAL PRESSLRE DROP I N SHELL ( P S I ) = 9F8.2) R I T E 2 3 0 1 0 0 8 FORMAT( lHO923HLOG-MEAN DELTA-T ( F ) = 9F7. Z T / / ~ R I T E 240

R I T E 250

1 ( F T 2 1 = 9F8 .11 R I T E 261

1E LENGTH ( B T U / H R - F T Z - F I = r F 7 . 2 , / / ) R I T E 271 R I T E 2 8 0

1 LENGTH ( F T 2 ) = 9F8 .11 R I T E 291

l F L E SPACE LENGTH (BTU/HR-FTZ-F)= r F 7 . 2 ) R I T E 301 END R I T E 31@

1005 FORMAT( l H O p 4 5 H I N S I D E DIAMETER OF EXCHANGER SPELL ( I N C H E S ) = 9F7.21 R I T E 210

1009 FORMAT( l H 0 9 2 6 H T O T A L TUBE LENGTH ( F E E T I = 9F7.21 1010 FORMAT( lHO,59HTOTAL HEAT TRANSFER AREA BASED CN TOTAL TUBE LENGTH R I T E 2 6 0

1011 FORMAT( l H 0 9 7 7 H O V E R A L L HEAT TRANSFER C O E F F I C I E N T BASED ON TOTAL T U B R I T E 270

1 0 1 2 FORMAT( l H 0 1 3 4 H T O T A L BAFFLE SPACE LENGTH ( F E E T ) = 9 F 7 . 2 ) 1013 FORMAT( l H 0 9 6 7 H T O T A L HEAT TRANSFER AREA BASED CN TCTAL BAFFLE SPACERITE 290

1014 FORMAT( 1HO985HOVERALL HEAT TRANSFER C O E F F I C I E N T BASED ON TOTAL B A F R I T E 300

SUBROUT I N E V ISCOS( T i P ETAP 1 TR = T + 4 6 0 o ETAT = . 1 8 9 E - O 0 * ( T R / 4 9 2 o ) s * o ~ * ( 1 , + 9 8 6 o / 4 9 2 . ) / ( 1 o + 9 8 6 o / T R J C A L L S V H ( 2 r P e T i V i H P T ) ETAP = 1 1 5 9 2 0 o * E T A T * ( V / ( V - . O l 2 ) 1 9 8 2 RETURN END

SUBROUTINE C O N D T ( T i P i C 0 N D ) TR = T + 4 6 0 . CALL S V H ( 2 i P t T i V i H P T ) COND = 1 .093E-06*TR**1 .45+28. 5 3 7 5 E - 0 4 / V * * l 0 2 5 RETURN END

SUBROUTINE SVH( N i P 9 T i S V O L i H P T C C M M O N / T P / P R E S ~ T E M P T M ~ i M2iNC l i N C 2 , X T i Y T G O T O ( l i 2 ) i N

1 C A L L T I P U T RETURN

2 PRES=P TEMP=T C A L L SPECV(SVOL1 CALL H ( H P T 1 END

V I S C O 10 V I S C O 20 V ISCO 30 V I S C O 40 V I S C O 50 V I S C O 60 V I S C O 70

CONDT 10 CONDT 20 CONDT 30 CONDT 40 CONDT 50 CONOT 60 a\

w w

SVH 10 SVH 20 SVH 30 SVH 40 SVH 50 SVH 60 SVH 70 SVH 80 SVH 90 SVH 100

. ’ (

SUBROUT I N E S P E C V ( A N S I COMMON/VOL/C (5160) COMMON/TP/PRES 1 TEMP 1 M 1 1 P 2 TNC 1 1 N C 2 1 x 1 r Y T T = ( T E M P - 5 5 0 0 - 1 OE-5 1 / 10 0 + 1 0 N C l = T X T = T - N C l N C 2 = N C l + 1

M l = P Y T = P - M l M 2 = M l + l

P=( PRES-3500 . - 1 OE-5 1 / 100 o+ 1

I F ( M 1 o L T 1oOR. M 1 oGT 4 ) 11 2 1 C A L L ERROR

3 C O N 1 I N U E 2 I F ( N C L . L T o l o O R o N C l o G T , 5 5 ) 113

Z 1 l = C ( M 1 i N C l ) 2 1 2 = C ( M 1 i N C 2 1 Z 2 1 = C ( M 2 v N C I ) Z 2 2 = C ( M 2 rNC2 1 X A = Z 1 1 + ( Z 1 2 - Z 1 1 ) * X T X B=L 2 1+( 222-2 2 1 1 *X T Y S E T = X A + ( X B - X A l *YT Y A= Z 11 + ( 22 1-Z 1 1 1 *Y T Y B = Z 1 2 + ( Z 2 2 - Z 1 2 ) * Y T X S E T = Y A+ (YB-YA ) * X T ANS=O, 5* ( Y S E T + X S E T ) R E T U R N E N D

S P E C V 10 S P E C V 20 S P E C V 30 S P E C V 40 S P E C V 50 S P E C V 60 S P E C V 70 S P E C V 80 S P E C V 90 S P E C 100 S P E C 110 S P E C 120 S P E C 130 S P E C 140 S P E C 150 S P E C 160 S P E C 170 S P E C 180 S P E C 190 S P E C 200 S P E C 210 S P E C 220 S P E C 230 S P E C 240 S P E C 250 S P E C 260 S P E C 270 S P E C 280

SUBROUTINE H(ANS1 C OMMON/H/C ( 5 960 I COMMON/TP/PR ES T T EMP t M 1 9 P 2 9 NC 1 t NC 2 TXT t YT Z l l = C ( M l v N C l ) Z 1 2 = C ( M L r N C 2 1 Z 2 l = C ( M2 T NC 1 J Z 2 2 = c ( M 2 T NC2 1 X A=Z 11+( Z L 2 - Z l l I * X T X B= 2 2 1+( 2 2 2 - 2 2 1 )*XT Y SET =XA+ ( XB-XA 1 * YT Y A=Z11+( 2 2 1 - 2 1 1 ) *YT Y B= Z 12+ ( 2 2 2- Z 1 2 1 * Y T XSET=YA+ ( Y 6 - Y A )*XT

RETURN END

ANS=Oe5*(YSET+XSET)

SUBROUTINE T I P U T COMMON/VOL/V (5 960) COMMON/H/H( 5 . 6 0 ) DO 1 J r 1 . 5 6 R E A D ( 509 1001 1 ( V ( I t J ) t I = ~ T 5 )

DO 2 J s l . 5 6 R E A D ( 5 0 r 1 0 0 2 1 ( H ( IT J 1 , I = l t 5)

RETURN END

1 1001 FORMAT(5E10.01

2 1002 FORMAT( 5E10.0)

H 10 H 2 0 H 30 H 40 H 50 H 60 H 70 H 80 H 90 H 100 H 110 H 1 2 0 H 130 H 140 H 150 H 160

J I P U T 10 T I P U T 20 T I P U T 30 T I P U T 40 T I P U T 5 0 T I P U T 60 J I P U T 70 T I P U T 80 T I P U T 90 T I P U 100 T I P U 110

A

13 9

I n t e me d i a te Va r i ab le s

The i n t e r m e d i a t e v a r i a b l e s used i n t h e SUPEX computer program a r e

l i s t e d below i n t h e o r d e r i n which t h e terms appear i n t h e program. The

u n i t s i n which the v a r i a b l e s a r e expressed i n the program a r e a s f o l l o w s

Temperature O F

Massy 1bm Lengthy f t

P r e s s u r e , l b f / i n . * Densi ty , lbm/f t3

V i s cos i t y l b / f t * h r

DELPTA T o t a l a l lowable p r e s s u r e drop i n t h e c o l d f l u i d ( s team) .

LOP1, LOP2, ... LOP11 Counters used i n t h e v a r i o u s i t e r a t i o n loops t o

DE LTH

DTPB

BSL

DTI

TCAV

PCAV

SPVl

DUM

SPV2

S PVAV

S PVG

VIS 1

VIS2

VISAV

V I S G

determine whether t h e loop h a s converged w i t h i n a c e r t a i n p r e - se t number of i t e r a t i o n s .

T o t a l temperature drop i n t h e h o t f l u i d ( s a l t ) .

Temperature drop i n t h e h o t f l u i d ( s a l t ) p e r b a f f l e space based on t h e e s t i m a t e d number of b a f f l e spaces (GNB).

B a f f l e spac ing l e n g t h .

I n s i d e d iameter o f tubes .

Average temperature o f t h e co ld f l u i d ( s team) .

Average p r e s s u r e of t h e co ld f l u i d (s team).

I n l e t s p e c i f i c volume of the co ld f l u i d (s team).

A dummy v a r i a b l e .

O u t l e t s p e c i f i c volume of t h e c o l d f l u i d (s team).

Average s p e c i f i c volume o f t h e c o l d f l u i d (s team).

A guess a t the mean v a l u e of the s p e c i f i c volume of the c o l d f l u i d (steam) used i n making an i n i t i a l e s t i m a t e o f t h e mass f low r a t e of t h e c o l d f l u i d .

I n l e t v i s c o s i t y of t h e c o l d f l u i d (s team).

O u t l e t v i s c o s i t y of t h e c o l d f l u i d ( s team) .

Average v i s c o s i t y of t h e c o l d f l u i d (s team).

A guess a t t h e mean v a l u e o f t h e v i s c o s i t y o f t h e c o l d f l u i d (s team) u s e d i n making an i n i t i a l e s t i m a t e of t h e Reynolds num- b e r f o r t h e c o l d f l u i d .

140

C FG

THETAL

PERCL

THETAU

PERCU

NEW

PNEW

EPNEW

THETAC

ti

REG

CFC

DIFA

NUMT

BNUMT

DS

A guess a t t h e v a l u e o f t h e f r i c t i o n f a c t o r f o r t h e c o l d f l u i d (s team).

The minimum v a l u e o f t h e a n g l e THETA ( r a d i a n s ) , where THETA i s h a l f o f t h e a n g l e subtended by t h e chord t h a t i s formed by t h e window r e g i o n o f t h e b a f f l e . The v a l u e 0.8 c o r r e s - ponds t o 0 = 4 5 " ; t h i s v a l u e i s j u s t a guess used t o s t a r t t h e i t e r a t i o n process .

The r a t i o o f t h e window area t o t h e t o t a l c r o s s - s e c t i o n a l a r e a a t t h e b a f f l e , based on THETAL.

The maximum v a l u e of t h e a n g l e THETA. cor responds t o 6 = 90 ' .

The r a t i o of t h e window area t o t h e t o t a l c r o s s - s e c t i o n a l area a t t h e b a f f l e , based on THETAU.

The v a l u e of THETA based on t h e i t e r a t i o n scheme.

The r a t i o o f t h e window a r e a t o t h e t o t a l c r o s s - s e c t i o n a l a r e a a t t h e b a f f l e , based on NEW.

The a b s o l u t e d i f f e r e n c e between t h e d e s i r e d f r a c t i o n a l window c u t (PW) and t h e c a l c u l a t e d f r a c t i o n a l window c u t (PNEW).

The c a l c u l a t e d v a l u e o f THETA t h a t g i v e s t h e d e s i r e d v a l u e of t h e f r a c t i o n a l window c u t .

Mass v e l o c i t y ( d e n s i t y times flow speed) f o r t h e co ld f l u i d (s team).

Reynolds number f o r t h e c o l d f l u i d (steam) based on a n e s t i m a t e o f t h e v i s c o s i t y o f t h e co ld f l u i d ,

C a l c u l a t e d f r i c t i o n f a c t o r f o r t h e c o l d f l u i d (s team).

Absolu te d i f f e r e n c e between t h e c a l c u l a t e d and guessed v a l u e s o f t h e f r i c t i o n f a c t o r f o r t h e c o l d f l u i d (steam).

Number of t u b e s r e q u i r e d .

F l o a t i n g p o i n t convers ion v a l u e of t h e i n t e g e r NUMT.

I n s i d e d iameter of t h e s h e l l of t h e h e a t exchanger ,

The v a l u e o f 1.5707

Y

14 1

XBAR

BRLl

GBRL

AW

AX

AXC

DIFB

THETA2

Axc2 GC

XB

CNB

D i s t a n c e from t h e i n s i d e s u r f a c e o f t h e s h e l l t o t h e c e n t r o i d of t h e window a r e a a t a b a f f l e .

X B A R 3 Tangent of t h e a n g l e @, a s i l l u s t r a t e d i n s k e t c h above.

(0.77/BRL1° f a c t o r developed t o modify B e r g e l i n ' s c o r r e l a t i o n i n c a s e s where t h e b a f f l e spac ing becomes l a r g e r e l a t i v e t o t h e d i a m e t e r of t h e s h e l l . I n such c a s e s , t h e flow i n t h e middle o f t h e b a f f l e r e g i o n i s e s s e n t i a l l y p a r a l l e l .

Window a r e a a t a b a f f l e .

B a f f l e a r e a ( t o t a l c r o s s - s e c t i o n a l a r e a minus window a r e a ) ,

A v a l u e o f AX c a l c u l a t e d from a v a l u e o f THETA.

Absolu te d i f f e r e n c e between AXC and AX.

A v a l u e o f t h e a n g l e THETA based on t h e v a l u e of AXC.

A v a l u e o f AXC based on t h e v a l u e o f THETA2.

Mass v e l o c i t y ( d e n s i t y times flow speed) f o r t h e co ld f l u i d (steam) based on t h e c u r r e n t number o f t u b e s i n t h e exchanger (NUMT) . D i s t a n c e from t h e a x i a l c e n t e r l i n e t o t h e window edge o f t h e b a f f l e .

Number o f rows of t u b e s from t h e window edge o f one b a f f l e t o t h e window edge o f t h e fo l lowing b a f f l e .

T h i s f a c t o r i s a m u l t i p l i c a t i v e c o r r e c t i o n

142

XH

CNW

xc PCFB

SBK

sw SDPT

SDPS

MS

RWK

I n s i d e r a d i u s o f t h e s h e l l minus XB.

Number of rows o f t u b e s i n one window.

Chord l e n g t h o f t h e window edge o f t h e b a f f l e .

F r a c t i o n of t h e d i s t a n c e between t u b e c e n t e r s t h a t i s f r e e f o r c r o s s flow.

Average f r e e a r e a i n c r o s s flow p e r u n i t b a f f l e spac ing .

F r e e h o t - f l u i d ( s a l t ) a r e a i n t h e window r e g i o n .

Summed p r e s s u r e drop on t h e t u b e s i d e ,

Summed p r e s s u r e drop on t h e s h e l l s i d e .

A c o u n t e r which h a s a v a l u e o f 1 f o r t h e f i r s t c a l c u l a t i o n i n each b a f f l e space and a v a l u e o f z e r o f o r t h e res t of t h e incrementa l c a l c u l a t i o n s i n t h e b a f f l e space .

Summed t u b e l e n g t h .

Summed b a f f l e space l e n g t h .

Temperature o f t h e c o l d f l u i d (steam) a t t h e beginning of t h e I - t h increment .

Temperature of t h e h o t f l u i d ( s a l t ) a t t h e beginning o f t h e I - t h increment .

A f a c t o r used t o c a l c u l a t e t h e h e a t t r a n s f e r r e s i s t a n c e of t h e t u b e w a l l m a t e r i a l . t h i c k n e s s o f t h e t u b e w a l l . I f

It can b e thought o f as a n e f f e c t i v e

d d

1

where

% = thermal r e s i s t a n c e o f t u b e w a l l m a t e r i a l ,

d = o u t s i d e d iameter of tube, 0

k = thermal c o n d u c t i v i t y of w a l l m a t e r i a 1 , a n d

d . = i n s i d e d iameter o f t u b e ; then 1

V

RWK = %k .

143

W

e

BN

QX DECT

DECH

I

K

SB

TCON

DENH

VISH

DHOT ( K)

VHOT (K)

CON 1

GM

RECB

H J B

HB

Gw

GS

mcw HJW

P r e s s u r e o f t h e co ld f l u i d (steam) a t t h e beginning of t h e I- t h increment .

Entha lpy o f t h e c o l d f l u i d (steam) a t t h e beginning o f t h e I - t h increment .

F l o a t i n g p o i n t convers ion of t h e i n t e g e r N ( c . f . i n p u t v a r i a b l e s ) .

The amount o f h e a t t o b e t r a n s f e r r e d i n each increment .

The change i n tempera ture p e r increment o f t h e h o t f l u i d ( s a l t ) .

The change i n e n t h a l p y p e r increment of t h e c o l d f l u i d (s team).

S u b s c r i p t index which r e f e r s t o t h e increments .

S u b s c r i p t index which r e f e r s t o t h e b a f f l e spaces .

T o t a l c ross - f low a r e a f o r t h e h o t f l u i d ( s a l t ) i n a g iven b a f f l e space.

An e s t i m a t e o f t h e b u l k tempera ture of t h e h o t f l u i d ( s a l t ) i n a b a f f l e space.

D e n s i t y o f t h e h o t f l u i d ( s a l t ) based on t h e tempera ture

V i s c o s i t y o f t h e h o t f l u i d ( s a l t ) based on t h e tempera ture

D e n s i t y o f t h e h o t f l u i d ( s a l t ) f o r t h e K-th b a f f l e s p a c e ,

V i s c o s i t y o f t h e h o t f l u i d ( s a l t ) f o r t h e K-th b a f f l e space .

The P r a n d t l number f o r t h e h o t f l u i d ( s a l t ) r a i s e d t o the 213 power.

Mass v e l o c i t y ( d e n s i t y times flow speed) o f t h e h o t f l u i d (salt) i n cross flow.

The c r o s s - f l o w Reynolds number f o r t h e h o t f l u i d ( s a l t ) .

The e f f e c t o f t h e c r o s s - f l o w Reynolds number on t h e s h e l l - s i d e c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t .

The s h e l l - s i d e c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t f o r c r o s s flow.

Mass v e l o c i t y ( d e n s i t y times flow speed) o f t h e h o t f l u i d ( s a l t ) i n p a r a l l e l flow.

A k i n d o f root-mean-square mass v e l o c i t y f o r t h e h o t f l u i d ( s a l t ) . It i s used i n t h e B e r g e l i n c o r r e l a t i o n s .

The p a r a l l e l - f l o w Reynolds number f o r t h e h o t f l u i d ( s a l t ) .

The e f f e c t o f t h e p a r a l l e l - f l o w Reynolds number on t h e s h e l l - s i d e c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t .

(TCON) . (TCON) .

144

Hw

TH( I+1)

DELPP

HCG

EH

TRIAL

HRIAL

TNEXT

DENOM

TDEN

DELTLM

TM

PM

S PVB

HFB

VISB

TMS

The s h e l l - s i d e convect ive hea t t rans f e r c o e f f i c i e n t f o r p a r a l l e l flow.

The t o t a l s h e l l - s i d e convect ive hea t t r a n s f e r c o e f f i c i e n t .

The f i lm r e s i s t a n c e t o hea t t r a n s f e r on t h e o u t s i d e of t h e tubes f o r t he K-th b a f f l e space.

Temperature of t h e hot f l u i d ( s a l t ) a t t h e end of t h e I - t h increment ( i . e . t h e beginning of t h e I+1-th increment).

Tube-side change i n p re s su re f o r a given increment.

An e s t ima te of t h e enthalpy of t h e cold f l u i d (steam) a t t h e end of t h e I - t h increment based on t h e est imated pressure and temperature a t t h e end of t h e I - t h increment.

The abso lu te d i f f e r e n c e between HCG and t h e HC(I+l) which has been ca l cu la t ed based on t h e hea t t r a n s f e r r e d p e r increment (QX/WC) . A t r i a l va lue of TC(I+l) t o be used f o r i t e r a t i o n .

A t r i a l va lue o f HC(I+l) t o be used f o r i t e r a t i o n .

A va lue of TC(I+l) which i s determined by t h e i t e r a t i o n scheme ( i . e . a new estimate of TC(I+l) t o s t a r t t h e next i t e r a t i o n ) ,

The a n t i l o g of t h e denominator of t h e de f in ing equat ion f o r a logar i thmic mean temperature d i f f e rence .

The abso lu te d i f f e r e n c e between DENOM and un i ty .

Logarithmic mean temperature d i f f e rence .

Average temperature of t h e cold f l u i d (steam) i n t h e I - t h increment . Average pressure of t he cold f l u i d (steam) i n t h e I - t h inc re - men t . Spec i f i c volume of t h e cold f l u i d based on t h e average temperature and pressure , TM and PM, i n t h e increment.

Enthalpy of t h e cold f l u i d (steam) based on t h e average temperature and pressure, TM and PM, i n t h e increment,

V i scos i ty of t h e cold f l u i d (steam) based on t h e average temperature and pressure , TM and PM, i n t h e increment.

Temperature of t he w a l l ma te r i a l i n t h e increment.

Thermal conduct iv i ty of t he w a l l m a t e r i a l i n t h e increment.

Thermal r e s i s t a n c e of t h e wal l m a t e r i a l i n t h e I - t h increment.

Di f fe rence between temperature of i n s i d e wa l l and temperature of bulk cold f l u i d (steam) f o r t h e increment.

Mean temperature of t h e tube wa l l su r f ace i n t h e increment.

W

I

145

SPVI

HFI

TCFI

VISFI

CRE

CPR

csv

DTFMC

DTFM2

TMs2

S p e c i f i c volume of t h e co ld f l u i d (steam) based on t h e average p r e s s u r e and mean tube-wall s u r f a c e tempera ture , PM and TMS, i n t h e increment .

Entha lpy of t h e c o l d f l u i d (steam) based on t h e average p r e s s u r e and mean tube-wal l s u r f a c e tempera ture , PM and TMS, i n t h e increment .

Thermal c o n d u c t i v i t y o f t h e c o l d f l u i d (steam) based on t h e average p r e s s u r e and mean tube-wall s u r f a c e tempera ture , PM and TMS, i n t h e increment .

V i s c o s i t y o f t h e c o l d f l u i d (steam) based on t h e average p r e s s u r e and mean tube-wal l s u r f a c e tempera ture , PM and TMS, i n t h e increment .

Reynolds number o f t h e co ld f l u i d (s team), based on t h e i n s i d e t u b e w a l l c o n d i t i o n s , r a i s e d t o t h e 0.923 power.

P r a n d t l number o f t h e c o l d f l u i d , based on i n s i d e t u b e w a l l c o n d i t i o n s and a f i c t i t i o u s s p e c i f i c h e a t , r a i s e d t o t h e 0.613 power. The f i c t i t i o u s s p e c i f i c h e a t i s d e f i n e d a s

where H i s en tha lpy , T is tempera ture and t h e s u b s c r i p t s " i l l and "b" r e f e r t o i n s i d e t u b e s u r f a c e and bulk c o l d f l u i d ( s team) , r e s p e c t i v e l y . This d e f i n i t i o n o f s p e c i f i c h e a t i s necessary s ince s p e c i f i c h e a t a s normally d e f i n e d i s inde terminant a t t h e c r i t i c a l p o i n t , w h i l e en tha lpy , a l though d i s c o n t i n u o u s a t t h e c r i t i c a l p o i n t , i s n o t inde terminant .

The r a t i o o f t h e bulk s p e c i f i c h e a t of t h e c o l d f l u i d (steam) t o t h e s p e c i f i c h e a t o f t h e co ld f l u i d eva lua ted a t i n s i d e tube-wal l c o n d i t i o n s r a i s e d t o t h e 0.231 power.

Convect ive h e a t t r a n s f e r c o e f f i c i e n t o v e r t h e increment f o r t h e i n s i d e s u r f a c e o f t h e t u b e w a l l .

The thermal r e s i s t a n c e of t h e c o n v e c t i v e f i l m on t h e i n s i d e s u r f a c e of t h e tubes , f o r t h e I - t h increment , a d j u s t e d t o t h e o u t s i d e d iameter of t h e tube .

The t o t a l thermal r e s i s t a n c e between t h e h o t ( s a l t ) and c o l d (steam) f l u i d s f o r t h e I - t h increment .

The tempera ture drop a c r o s s the i n s i d e t u b e w a l l c o n v e c t i v e f i l m f o r t h e increment .

A r i t h m e t i c average o f DTFM and DTFMC.

New estimate o f t h e mean tube-wall s u r f a c e tempera ture based on DTFM2.

146

SPVI2

HFI2

TCFI2

VISFI2

cRE2

CPR2

c s v 2

H2 I

R2 I

U T

DTFMCZ

SLOPE

CFI

DELP ( I)

DIFC

IBK(K)

New estimate o f t h e s p e c i f i c volume o f t h e c o l d f l u i d (steam) based on a v e r a g e p r e s s u r e (PM) and the new estimate o f t h e mean tube-wall s u r f a c e tempera ture (TMS2) f o r t h e increment . New e s t i m a t e o f t h e e n t h a l p y of t h e c o l d f l u i d (steam) based on t h e average p r e s s u r e (PM) and t h e new estimate o f t h e mean tube-wal l s u r f a c e tempera ture (TMSZ) f o r t h e increment .

N e w e s t i m a t e of t h e thermal c o n d u c t i v i t y o f t h e c o l d f l u i d (steam) based on t h e average p r e s s u r e (PM) and t h e new e s t i m a t e o f t h e mean tube-wall s u r f a c e tempera ture (TMS2) f o r t h e increment .

New e s t i m a t e o f t h e v i s c o s i t y of t h e c o l d f l u i d (steam) based on t h e average p r e s s u r e (PM) and t h e new estimate o f t h e mean tube-wall s u r f a c e tempera ture (TMS2) f o r t h e increment .

New e s t i m a t e o f CRE based on VISFI2.

New e s t i m a t e o f CPR based on HFI2, TMS2, VISFI2, and TCFI2.

New e s t i m a t e of CSV based on SPVI2.

New e s t i m a t e of H I based on TCFI2, CRE2, CPR2, and CSV2.

New estimate o f RI(1) based on H2I.

New estimate of RT(1) based on R2I.

New e s t i m a t e o f DTFMC based on R Z I and R2T.

A r a t i o o f two d i f f e r e n c e s between v a r i o u s e s t i m a t e s o f t h e tempera ture drop a c r o s s t h e i n s i d e t u b e w a l l c o n v e c t i v e f i l m f o r t h e increment . T h i s i s used t o make a new e s t i m a t e of DTFM i n o r d e r t o c o n t i n u e t h e i t e r a t i o n p r o c e s s .

O v e r a l l h e a t t r a n s f e r c o e f f i c i e n t f o r t h e I - t h increment based on t h e o u t s i d e d iameter of t h e t u b e ,

Tube l e n g t h i n t h e I - t h increment .

Reynolds number f o r t h e c o l d f l u i d (steam) based on t h e bulk v i s c o s i t y (VISB) o f t h e increment ,

Fanning f r i c t i o n f a c t o r f o r t h e c o l d f l u i d (steam) f o r t h e increment ,

The p r e s s u r e drop f o r t h e co ld f l u i d (steam) i n t h e I - t h increment ,

The d i f f e r e n c e between two c o n s e c u t i v e v a l u e s o f t h e p r e s s u r e drop f o r t h e c o l d f l u i d i n t h e I - t h increment a s determined by c o n s e c u t i v e p a s s e s through t h e i t e r a t i o n loop.

The v a l u e o f t h e index I a t t h e beginning o f t h e f i r s t increment t h a t i s t o t a l l y conta ined w i t h i n t h e K-th b a f f l e space.

c

147

ALPHA

ETW

CON2, CON3

B, SL

CON4

TWALL (K)

DELTWA (K)

DELTW (K)

BWN

W

DELPSB

DELPSW

DELPS (K)

EDPT

EDPS

J, J N , J N C

NBS

I N , I N C

AREAX

UEQX

AREAB

UEQB

Coef f i c i en t of thermal expansion f o r t h e tube w a l l m a t e r i a l (x 106).

Modulus of e l a s t i c i t y f o r t h e tube wal l m a t e r i a l (x

Fac to r s i n t h e expression which c a l c u l a t e t h e s t ress components i n t h e tube wa l l .

Constants i n t h e express ion given i n Sec t ion I11 of t h e ASME Bo i l e r and P res su re Vessel Code f o r c a l c u l a t i n g t h e allow- a b l e thermal s t r e s s components.

Te rm f o r t h e al lowable thermal s t r e s s components given i n Sec t ion I11 of t h e ASME Boi l e r and P res su re Vessel Code.

Temperature of tube wa l l m a t e r i a l f o r t h e K-th b a f f l e space.

Allowable temperature d i f f e r e n c e ac ross t h e tube wa l l f o r t h e K-th b a f f l e space based on a l lowable thermal stresses.

Temperature d i f f e r e n c e ac ross t h e tube w a l l f o r t h e K-th b a f f l e space.

Fac tor used i n s h e l l - s i d e pressure drop c a l c u l a t i o n s . The f a c t o r t akes t h e va lue 0.5 i f t h e increment i s a t e i t h e r end o f t h e exchanger, and i t t akes t h e va lue of u n i t y f o r a l l o t h e r increment p o s i t i o n s .

S h e l l - s i d e p re s su re drop i n the b a f f l e space a rea .

S h e l l - s i d e p re s su re drop i n t h e window area .

T o t a l s h e l l - s i d e pressure drop f o r t h e K-th b a f f l e space.

Absolute d i f f e r e n c e between t h e t o t a l c a l c u l a t e d tube-s ide p re s su re drop and t h e a l lowable t o t a l tube-s ide p re s su re drop.

Absolute d i f f e r e n c e between t h e t o t a l c a l c u l a t e d s h e l l - s i d e pressure drop and the allowable total shell-side pressure drop.

Counters t o put t h e b a f f l e space information ou t i n groups of 50 p e r page.

To ta l number o f b a f f l e spaces.

Counters t o p u t t h e increment information ou t i n groups of 50 per page.

The f i l m r e s i s t a n c e t o hea t t r a n s f e r on t h e o u t s i d e of t h e tubes f o r t h e I - t h increment.

To ta l h e a t t r a n s f e r a r ea based on t o t a l tube length.

Overall h e a t t r a n s f e r c o e f f i c i e n t based on t o t a l tube length .

To ta l hea t t r a n s f e r a r ea based on t o t a l b a f f l e space length .

Overal l hea t t r a n s f e r c o e f f i c i e n t based on t o t a l b a f f l e space length .

148

Subrout ines

There a r e t e n subrout ines i n t h e SUPEX computer program. The terms

used f o r each of t hese subrout ines a r e l i s t e d below wi th a b r i e f

d e s c r i p t i o n of t h e purpose of each subrout ine.

RITE1 Writes out t h e input information.

RITE2 Wri tes ou t d e f i n i t i o n s of t h e va r ious columns i n t h e t a b l e of ou tput f o r each b a f f l e space,

RITE3 Writes out d e f i n i t i o n s of t h e va r ious columns i n t h e t a b l e o f ou tput f o r each increment.

p r o p e r t i e s f o r t h e e n t i r e exchanger.

f o r a given temperature and pressure .

f l u i d (steam) f o r a given temperature and pressure .

subrout ines SPECV and H when N = 2.

RITE4 Wri tes ou t information concerning t h e average o r t o t a l

VISCOS(T, P, ETAP) Ca lcu la t e s t h e v i s c o s i t y of t h e cold f l u i d (steam)

CONDT(T, P, COND) Ca lcu la t e s the thermal conduc t iv i ty of t h e co ld

SVH(N,P,T, SVOL, HPT) Ca l l s t h e subrout ine TIPUT when N = 1 o r c a l l s

SPECV(ANS) Ca lcu la t e s , using an i n t e r p o l a t i o n of input da t a , t h e

H (ANS 1 Calcu la t e s , us ing an i n t e r p o l a t i o n o f input da t a , t h e

TIPUT Reads i n an a r r a y of va lues of s p e c i f i c volume and s p e c i f i c

s p e c i f i c volume of t h e cold f l u i d (steam).

s p e c i f i c enthalpy of t h e cold f l u i d (steam).

en tha lpy a s func t ions o f temperature and pressure .

c

Computer I n p u t and Output f o r Reference MSBR Steam Generator S u p e r h e a t e r

* * * THE FOLLOWING IS THE I N P U T INFORMATION FOR T H I S PROBLEM * *

OUTSIDE DIAMETER OF TUBES (INCHESI;. 0.500

TUBE M A L L THICKNESS ( INCHES t = 0.0770

TUBE P I T C H ( INCHES I = 0 .8750

NJM6ER OF INCREMENTS I N T O WHICH THE EXCHANGER I S D I V I D E D = 100

I N L E T TEMPERATURE OF HOT F L U I D ( F t = 1150.0

W T L E T TEMPERATURE OF HOT F L U I D ( F t = 850.0

I N L E T TEMPERATURE OF COLD F L U I D ( F t = 700.0

W T L E T TEMPERATURE OF COLD F L U I D ( F t = lCOO.O

W T L E T PRESSURE OF COLD F L U I D ( P S I ) = 3603.C

ALLOWABLE TOTAL PRESSURE DROP ON TUBE S I D E ( P S I t - 150.0

ALLOWABLE TOTAL PRESSURE DROP ON SHELL S I D E ( P S I ) = 60.0

MASS FLOW RATE OF COLD F L U I D ( L B / H R ) = 6.330E 0 5

MASS F L O k RATE OF HOT F L U I D ( L B / H R I = 2 .820E 06

TOTAL HEAT TRANSFER RATE ( B T U / H R t = 4.12CE 0 8

S P E C I F I C HEAT CF HOT F L U I D ( B T U / L B - F t = C.360

THERMAL CONDUCTIVITY OF HOT F L U I D (BTU/HR-FT-F t = 0 . 2 4 0

FRACTIONAL WINDOW CUT= 0.40

Computer Input Data for Reference MSBR Steam Generator Superheater (continued)

BY-PASS LEAKAGE FACTOR FOR PRESSURE= 0.520

BY-PASS LEAKAGE FACTOR FOR HEAT TRANSFER= 0. BOO

ESTIMATE OF THE NUMBER OF BAFFLE SPACES REQUIRED= 18

ESTIMATE OF THE LENGTH OF A BAFFLE SPACE(FTJ= 3.00

ESTIMATE OF THE TOTAL TUBE LENGTH(FTl= C5.00

(. I .

I I

r

‘ (

J

1 S T - 1

DELT-d

DELT-U-A

T - *ALL

DELP-S

DENS-H

V I SC-H

* * * T H E F O L L O W I N G T A B L E G I V E S I N F O R M A T I O N FOR EACH B A F F L E SPACE THROUGH THE EXCHANGER * * * THE COLUMN L A B E L S FOR T H I S T A B L E ARE D E F I N E D BELOW

B A F F L E SPACE NUMBER

I N C R E M E N T NUMBER OF F I R S T INCREMENT W H I C H L I E S COMPLETELY I N B A F F L E S P A C E J

C A L C U L A T E D TEMPERATURE DROP ACROSS TUBE WALL (FJ

ALLOWABLE TEMPERATURE DROP ACROSS T U B E WALL B A S E D C h ALLOWABLE S T R E S S ( F J

WALL M A T E R I A L TEMPERATURE ( F 1

C A L C U L A T E D S H E L L PRESSURE DROP FOR THE B A F F L E SPACE ( P S I )

M E A N D E N S I T Y O F THE HOT F L U I D FOR T H E B A F F L E SPACE ( L B I F T 3 )

M E A N V I S C O S I T Y O F THE HOT F L U I D FOR THE B A F F L E SPACE ( L B / F T - H R J

1 1 2 5 3 10 4 15 5 20 6 26 7 32 8 38 9 44

10 51 11 57 12 63 13 69 14 74 1 5 79 16 84 17 89 18 93 19 97

OELT-W ------- 53.05 61.14 70.73 78.72 86.7@ 94.22

100.01 104.06 106.05 105.97 103.91 100 40 95.38 90.69 85.40 80.07 74.71 70.78 67.2 7

DELT-W-A --- ---- - S0.73

1C6.37 121.2c 124.90 128.62 132.70 136.45 139.87 142.89 145.94 148.16 150.07 151.64 152.83

154.92

156.83

153.88

155.94

157.81

1 - h A L L - -- -- - 1061.5 1036.8 1007.0

579.9 S53.0 923.9

873.5 e52.6 831.8 €16.8 803.9 793.4

778.5 771.7 765.0 7 59.1 752.7

857.4

785.5

D E L P - 5 ------ 1.785 3.391 3.380 3.364

3.345 3.332 3.320 3.307 3.292 3.280 3.268 3.255 3.245 3.235 3.225 3.21 5 3.207 3.1 99

3.358

DENS-H ------ 113.2 113.5 113.9 114.3 114.6 115.1 115.5 116 -0 116.4 116.9 117.4 117.8 118.3 118.6 119.0 119.4 119.7 120.0 120.3

V I SC-H ------ 2.630 2.681 2.746 2.815 2.886 2.976 3.071 3.172 3.278 3.411 3.531 3.660 3.796 3.917 4.044 4.178 4.320 4.439 4.564

I

LENGTH

T-HOT

1-COLD

P-COLD

OELP-C

R E S - I N

RES-WALL

RES-OUT

RES-TOT

* * * THE FOLLOWING TABLE G I V E S INFORMATION AT EACH INCREMENT THROUGH THE EXCHANGER * * THE CCLUMh L A B E L S FOR T H I S T A e L E ARE D E F I N E D BELOW

INCREMENT NUMBER

TUBE LENGTH FOR THE INCREMENT ( F E E T )

TEMPERATURE OF THE HOT F L U I D ( F I

TEMPERATURE OF THE COLD F L U I D ( F I

PRESSURE OF THE COLD F L U I D ( P S I 1

TUBE PRESSURE ORCP FOR THE INCREMENT ( P S I 1

THERMAL RESISTANCE OF THE I N S I D E F I L M FOR THE INCREMENT (HR-F/BTU)

THERMAL RESISTANCE OF THE WALL MATERIAL FOR THE INCREMENT (HR-F/BTU) F cn h) THERMAL RESISTANCE OF THE OUTSIDE F I L M FOR THE BAFFLE SPACE I N WHICH THE INCREMENT L I E S ( H R - F / B T U l

TOTAL THERMAL RESISTANCE BETWEEN HOT E COLD F L U I D S FGR THE INCREMENT (HR-F/BTU)

I LENGTH T-HOT T-COLD P-COLD DELP-C ---- 1 2 3 4 5 6 1 0 9

10 1 1 12 13 14

-a_--- - 1.016 1 e038 1 .0c 2 0 .975 0 0 9 5 1 0 0 9 2 4 0 0 8 9 9 0 .882 0 0 8 5 9 0 .839 0 .824 0 .809 0 .794 0.180

.----- - 1150.0 1141.0 1144.0 1141.0 1138.0 1135.0 1132.0 1129.0 1126.0 1123.0 1120.0 1117.C 1114.0 1 1 1 1 . 1

1c00 .0 993.5 $82 .9 576.4 967 .9 961 .4 952 .4 945 .9 939 .4 930 .3 923.8 917 .3 9112.8 $04 .3

3600.0 3604.4 3608.5 3612.5 3616.3 3620.0 3623.5 3626.9 3630.2 3633.3 3636.4 3639.3 3642.1 3644.9

------ 4 .390 4 .173 3 .979 3.021 3.619 3 .520 3 .385 3 .279 3.147 3.030 2.937 2.845 2 .156 2.670

R E S - I N -------- 0.000476 0 0004 13 0 .000469 0.000464 O.OQ0460 0.000455 ‘3.00@45 1 0. 000441 0.000442 0 .000430 0.000434 0.000429 0. 000424 0.000420

RES-WALL -------- 0.000721 0 .000724 0 00012 7 0 .000130 o . o o a i 3 3 0 .000736 0 .000139 0 .000142

0 .000740 0 00015 1 0 00015 3 0 0001 56 0 -000759

a. 000745

RES-OUT -------- 0 -000842 0 .000842 0 .000042 0 .000042 0.000 847 0 .000047 0 000 847 0 o000841 0 000 0 4 1 0 ,000853 0.000853 0 .000853 0 .000853 0 .000053

RES-TOT -------- 0 -00 2039 0 -00 2039 @ -002039 C 0 0 2037 0 .002039 0.002038 0 00 2036 0.002036 0 00 2034 0 .@02@30 0oO02031 0.002035 O.QQ2033 0 .OQ2@3L

c ’ I

15 16 17 18 19

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 5 5 56 57 58 59 60 6 1 62

20

0.768 0.755 0 0742 0.729 0.110 0.710 0 -70 1

0.606 0 -694

0 e679 0.672 0.660 0.662 0.657 0.652 0.647 0.643 0.641 0.637 0 e634 0.631 0.620 0.626 0 -626 0.625 0.623 0.622 C,.621 0 e620 0.622 0.622 0 623 0 e623 0.624 0.624 0.625 0.630 0.632 0.635 0.637 0 -639 0 e642 0 649 0.652 0.655 0.659 0 663 0.660

1108.1 1105. 1 1102.1 1099. 1 1096. 1 1093.1 1090 1 1087.1 1084.1 1081.1 1078.1 1075.1 1072.1 1069.1 1066. 1 1063.1 1060.1 1057.1 1054.1 1051.1 1048.1 1045 1 1042.1 1039.1 1036.1 1033.2 1030.2 1027.2 1024.2 1021.2 1018.2 1015.2 1012.2 1009 2 1006.2 1003. 2 1000.2 997.2 994.2 991 2

985.2 982.2 979.2 976.2 973 2 970.2 967.2

see. 2

897.8 891.3 084.7 078.2 871.7 866.3 059.8 855. c e49.0 844.5 839.3 834.5 829.7 824.9 820.2 815.9 811.7 807.6 803.4 799.5 795..7 792.1 780.6 785.2 781.9 178.9 775.9 773.0 770.3 767.8 765.2 762.8 760.6 750.5 756.4 754.4 752.7 750.7 749.3 747.9 746.5 745.1 744.0 742.7 741.4

739.3 730.5

740. o

3647.6 3650.2 3652.7 3655.1 3657.5 3659.7 3662.0 3664.1 3666.2 3668.3

3672.2 3674.1

3677.8

3C81.3

3670.3

3676.0

3C79.6

3683.0 3604.7 3686.3 3687.9

3691.0 3692.5 3t93.9 3695.4 3696.8 3698.2 3699.5 3700.9 3702.2 3703.4

3689.5

3704.7

3707.2 3708.3 3709.5 3710.7 3711.8

3705.9

3712.9 3714.0 3715.1 3716.2

3710.3 3 717.3

3719.3 3720.3 3721.3

2.592 2.510 2.430 2.350 2.202 2.223 2.161 2.109 2.054 2.002 1.950 1.909 1 862 1.818 1.775 1.734 1.694 1.662 1 626 1.590 1.556 1.523 1.490 1.464 1.436 1.407 1.379 1.353 1.328 1.307 1.282 1 260 1.239 1.215 1.193 1.173 1.159 1.142 1.123 1.104 1.086 1 071 1.061 1.044 1.027 1.010 0.995

0 0004 14 0 000409 0.000404 0.000398 0.000392 0.00038 7 0.000381 0.000376 0.0003 71 0.000366 0.000360 0.000354 0.000349 0.000344 0 0003 38 0 .000332 0 0003 25 0 0003 19 0.00C314 9.000309 0 000 30 3 0.000297 0 000290 0.C00204 0 .000 2 80 0 . COO2 73 OeC00267 0. COO26 1 0.0002 54 0.000247 0 *OO0241 0.000236 O.OC’O230 0 000 223 0.000216 0 .0002 10 0 000205 0 . 00C 199 0.000193 0.000186 0.000179 0.000174 0 000 160 0.000 163 0.000157 0.0001 52 0 000 145

0.982 0.000139

0 00076 1 0.090764 0.000767 0.000770 O.CO0772 0.000 775 0.000778 0.00070C 0.000702 0.000185 0.000787 0.000789 0 00079 2 0.000794 0. 000796 0.000798 0 . 000 80 0 0.000 80 2 0.003804 0 000 80 6 c.000808 0.000810 0 .om81 2 0 000814 0.00081 5 0.0008 17 0.000819 0.1)00020 0*000822 0.000 82 3 0.000825 0 000 026 0.000027 0 . C0 0029 o .000830 0.00003 1 0.000832 0 e000834 0.000835 0.000836 0.000837 0.009838 0 . QOO039 0.000840 0. COO841 0.90084 1 C 00004 2 0 000843

0 -000859 0 eOOO059 0.000859 0 -000859 0 -000859 0 000 86 5 0.000065 0.000065 0 e000865 0 e000865 0 -000 065 0.@00872 0 .OOO872 o.oaoa72 0 e000072 0 000 07 2 0.000072 0 00‘28 80

0.000880 0.000880 0 . 000 0 80 0 000800 0 .000888 0 . 000008 0.000888 0.000088 0 .000888 0 .000 8 0 8 0 -000897 0 0000 897 0 000 897

0 . ooa88o

0.000897 0.000897 0.000897 0 -000 897 0.000907 0 .00@907 0 A0090 7 a . ooo 907 0 e000 9C 7 0 000907 0.000916 0 eQOC916 0 . 0009 16 0.000916 0 000916 0.000916

0 0 0 20 34 0.002032 0 e 0 0 2030 0.002026 0.002023 0.002027 0 -00 2024 0.002021 0.00 201 8 0 -0 0 20 15 0.00201 1 0 .002C16 0.002012 0.00201c 0 002006 @ 00 2002 0 00 1996 ‘0. Q@ 2002 0.0 91998 0.00 1995 0 0 C 1991 00001907 0 -00 1981 O.OC1986 0 CO 1983 0.0 C 1979 O.CO1974 0.00 1969 0 -00 1964 0.00 1967 0.00 1963 9.0 01 558 C. C 0 1954 0.0 C 1949 0 -00 1943 0 - 0 0 1938 0 0 0 1 944 0.0 0194C 0.001935 0.0 C 1928 0 00 1923 0.001918 0 -0 0 1923 0.001918 0 001914 0 00 1909 0 00 1903 0 e 0 01898

6 3 C.677 6 4 0 . 6 8 2 6 5 C.687 6 6 0 . 6 9 3 6 7 0 . 6 9 9 6 8 C.706 6 9 0 . 7 1 6 70 0 . 7 2 3 7 1 0.73C 72 0 . 7 3 8 7 3 0 . 7 4 6 7 4 0 . 7 5 6 75 0 . 7 6 5 76 0 . 7 7 4 7 7 0 . 7 8 4 78 0 . 7 9 3 7 9 C.807 8C 0 . 8 1 7 81 C.828 82 0.838 83 0 . 8 4 9 04 0 . 8 6 5 85 0 . 8 7 6 86 00888 8 7 0 . 9 0 1 88 0 . 9 1 3 8 9 C.931 90 0.944 91 0 . 9 5 6 92 0 . 9 6 8 9 3 0 . 9 8 5 94 0 . 9 9 9 9 5 l e 0 1 4 9 6 1 .027 9 7 1 .040 9 8 1 . 0 4 9 99 1eC57

100 1 .066

9 6 4 . 2 7 3 7 . 8 9 6 1 . 2 7 3 7 . 2 9 5 8 . 3 7 3 6 . 5 9 5 5 . 3 735 .7 9 5 2 . 3 735 .0 9 4 9 . 3 7 3 4 . 3 9 4 6 . 3 7 3 3 . 7 9 4 3 . 3 733 .0 9 4 0 . 3 7 3 2 . 3 9 3 7 . 3 731 .6

9 3 1 . 3 7 3 0 . 3 9 3 4 . 3 7 3 1 . 0

9 2 8 . 3 729 .7 9 2 5 . 3 729.0 9 2 2 . 3 728 .4 4 1 9 . 3 7 2 7 . 8 9 1 6 . 3 7 2 7 . 2 9 1 3 . 3 726.5 9 1 0 . 3 7 2 5 . 9 9 0 7 . 3 7 2 5 . 3 9 0 4 . 3 7 2 4 . 7 9 0 1 . 3 724. C 8 9 8 . 3 7 2 3 . 4 8 9 5 . 3 722 .7 892 3 7 2 2 . 0 8 8 9 . 3 721 .4 8 8 6 . 3 720 .7 8 8 3 . 3 720. 1 880 4 7 1 8 . 6 8 7 7 . 4 7 1 7 . 1 8 7 4 . 4 7 1 5 . 6 8 7 1 . 4 7 1 4 . 0 8 6 8 . 4 712 .7 8 6 5 . 4 71 1 .2 8 6 2 . 4 7 0 9 . 3 8 5 9 . 4 706 .9 8 5 6 . 4 704 .5 8 5 3 . 4 702. 0

3 7 2 2 . 3 3 7 2 3 . 3 3 7 2 4 . 3 3725.2 3726.1 3727.1 3728.C 3728.9 3729.8 3730. 6 3731 5 3 7 3 2 . 4 3 7 3 3 . 2 3 7 3 4 . 1 3134.9 3 7 3 5 . 7 3 7 3 6 . 5 3 7 3 7 . 3 3 7 3 8 . 2 3 7 3 9 . 0 3 7 3 9 . 8 3 7 4 0 . 6 3 7 4 1 . 4 3742.1 3 7 4 2 . 9 3 7 4 3 . 7 3744.5 3 7 4 5 . 2 3 746 .0 3 7 4 6 . 8 3747.5 3 7 4 8 . 3 3 7 4 9 . 0 3 7 4 9 . 8 3 7 5 0 . 5 3 7 5 1 . 3 3752.0 3 7 5 2 . 8

0 . 9 7 5 0 . 9 6 3 0 . 9 4 8 0 . 9 3 5 0 . 9 2 2 0.909 0 . 9 0 2 0 . 8 8 9 0 . 8 7 7 0 . 8 6 5 0.. 853 n. 845 0 . 8 3 8 0 . 8 3 1 0 . 8 2 6 0 . 8 2 1 0.818 0 . 8 1 2 0 . 8 0 7 a. 802 0 . 7 9 6 0 . 7 9 4 0 . 7 8 7 0 . 7 8 @ 0 . 7 7 4 0 . 7 6 8 a. 765 c. 760

a. 756

a. 754

0 . 7 5 8 0 . 7 5 5

0 . 7 5 5

0 . 7 5 0 0 . 7 5 0 0 . 7 4 6 0 . 7 4 2 0 . 7 3 9

RES-IN -------- 0 e 000 1 34 0 0001 2 9 0 COO 1 23 0 . 0 0 0 1 1 9 O.OCO1 15 0 .009111 0 OOOlO7 0.000 104 0. coo 10 1 0 OOOO99 O . C O O C 9 6 0. COO092 O.OOCC91 O.QOOC90 0.00C089 0.0000 88 0.OG0087 0 OOQC 86 0 .000085 0 . 00 00 8 4 a . coo083 0 . a000 02 0.000c 8 1 0. coo0 80 0.0000 80 0. 0oc 0 80 O.OGOC80 0 000@ 82 0 . oooc 88 0. COnOSft 0.000 100

0.000 1 1 4 0.000 122 0.000 127 C. 000 134 0 000 1 4 1 0 .000149

a. 000 i o 7

0.000 844

0 . 0 0 0 8 4 5

0.000 84 7

o . o o o a 4 4

0 . 0 0 0 8 4 6

0 . 0 0 0 8 4 7 0 . 0 0 0 8 4 8 0 . 0 0 0 8 4 9 0 .a00849 o.ooa85a

o. 0 0 0 8 5 2 0 . 0 0 9 8 5 1

0 . 0 0 0 8 5 2 c. c o o 0 5 3 Oo000854 0.000 854 0 . 0 0 0 8 5 5 o.000856 0 00085 7 Oo000857 0.0008 50 O.COO859 0 0 0 0 8 5 9 0 . 0 0 0 8 6 0 0 . 0 0 0 8 6 1 0 0 0 0 0 6 2 C 000 862 0 . 0 0 0 8 6 3 0 . 0 0 0 8 6 5 0 . 0 0 0 8 6 6 0 . 0 0 0 8 6 7 0 , 0 0 0 8 6 8

0 . 0 0 0 8 7 0 0 . 0 0 0 8 6 9

0 * 0 0 0 8 7 2 0 . 0 0 0 0 7 3 0 . 0 0 0 0 7 5 0 . 0 0 0 8 7 7

0 . 0 0 0 9 2 5 0 . 0 0 0 9 2 5 0 . 0 0 0 9 2 5 0 C O O 9 2 5 0 0 0 0 9 2 5 @ oOOO92 5 0 . 0 0 0 9 3 5

0 eOOC935 0 . 0 0 0 9 3 5 G e000935 0 OOn943 0 0 0 0 9 4 3 0 0 0 0 0 9 4 3 0 .COO943 0 C O O 9 4 3 0 . 0 0 0 9 5 2 0 . 0 0 0 9 5 2 0 . 0 0 0 9 5 2 0 . C O O 9 52 O.CO0952 c1.000961 0 e00096 1 0 .00@96 1 0 . 0 0 0 9 6 1 0 . 0 0 0 9 6 1 0 . 0 0 0 9 7 0 0.0009m 0 . 0 0 0 9 7 0 0 . 0 0 0 9 7 0

0 .000935

o .om 978 O.CO0978 0 e000978 0 e000978 Po000985 O.OC0985 0 . 0 0 0 9 8 5 0 . 0 0 0 9 8 5

RE S-TOT -------- 0 e 00 1903 0 e00 1898 0 -00 1893 0 .OC 1890 OoOO1 887 0 001 884 0.0 Cle90 0 . 0 0 1 8 8 8 O.GC1886 0.00 1884 0 .001882

O.FO1887 0.00 1887

3 000 1886 0 000 1886 0 .001885 0.00 1 e94 0 .oa 1894 0 . OC1893 O.OC1893 0 .001892 0 00 190 1 0 . 00 1901 0 .OC 1901 0 . 00 1902 0 .001902 0 .001912 0 . 0 0 1 9 1 5 0.00 1922 0 0 0 1929 0 -0 0 1945 0.0 C1953 0 . 0 0 1 9 6 1 9-00 197P 0 00 1984 0 0 0 1 9 9 2 0 . c 0 200 1 0 .00201 1

c

i 8

* * * THE FOLLOWING ARE AVERAGE O R TOTAL PROPERTIES FOR THE E N T I R E EXCHANGER * * *

TOTAL NUMBER OF TUBES= 393

TOTAL NUMBER O F @ A F F L E SPACES= 19

LEhGTH O F A B A F F L E S P A C I N G ( F T ) = 3.980

I N S I D E DIAMETER OF EXCHANGER SHELL ( I N C H E S ) = 1 8 . 2 1

TOTAL PRESSURE DROP IN TUBES ( P S I ) = 153.53

TGTAL PRESSURE DROP I N SHELL ( P S I ) = 61.01

LOG-MEAN DELTA-T ( F ) = 150.0C

TOTAL TUBE LENGTH ( F E E T ) = 76.38

TOTAL HEAT TRANSFER AREA BASED ON TOTAL TUBE LENGTH ( F T 2 ) = 3929.3

GVERALL HEAT TRANSFER C O E F F I C I E N T BASED ON TOTAL TUBE LENGTH ( B T U / H R - F T Z - F l = 699.02

TGTAL B A F F L E SPACE LENGTH ( F E E T ) = 75.61

TOTAL HEAT TRANSFER AREA BASED ON TOTAL BAFFLE SPACE LENGTH ( F T Z ) = 3889.9

OVERALL HEAT TRANSFER C O E F F I C I E N T BASED ON TOTAL B A F F L E SPACE LENGTH (BTU/HR-FTZ-F ) = 706.10

157

ORNL TM-2815

In t e rna 1 D i s t r i b u t i o n

1. J . L. Anderson 38 * 2 . C. F. Baes 3 9 . 3 . S . E . Bea l l 40. 4 . M. Bender 4 1 .

5 - 9 . C. E. Bett is 4 2 . 10. E . S . Bet t i s 4 3 . 11. E . G . Bohlmann 44. 1 2 . G. E . Boyd 4 5 1 3 . R. B . Briggs 4 6 . 1 4 . D. F. Cope (RDT S i t e Rep.) 47 0

15. W . K. Crowley 4 8 1 6 . J. R. Dis tefano 4 9 . 1 7 . S. J. D i t t o 5 0 1 8 . H. G. Duggan 5 1 - 6 0 . 1 9 . D . A. Dyslin 61. 20. W . P. Ea ther ly 6 2 . 2 1 . J. R. Engel 6 3 . 22 . D. E . Ferguson 6 4 . 2 3 . W . F. Ferguson 6 5 . 2 4 . L. M. F e r r i s 6 6 . 2 5 . F. C. F i t z p a t r i c k 6 7 . 26 . W . K. Furlong 6 8 .

2 8 . W . R. Gal l 7 0 . 2 9 . W . R. Grimes 71. 30. A. G. Gr inde l l 7 2 . 31. P. N . Haubenreich 7 3 . 3 2 . R. E . Helms 7 4 - 7 5 . 3 3 . P. R. Kasten 7 6 . 3 4 . R. J . Ked1 7 7 . 3 5 . J. J . Keyes 7 8 - 9 0 3 6 . K. 0 . Laughon (RDTSite Rep.) 9 1 . 3 7 . G . H. Llewellyn 9 2 .

27. C . H. Gabbard 69

M. I . Lundin H. G. MacPherson R. E . MacPherson H. E . McCoy H. A . McLain L. E . McNees J. R. McWherter A . S. Meyer R. J . Moore H. A. N e l m s E . L. Nicholson A. M. Perry T. W. P icke l M. W . Rosenthal Dunlap S c o t t M. Siman-Tov W . C . S toddar t R. E. Thoma D. B . Trauger H. K . Walker G. M. Watson H. L. Watts J. R. Weir M. E . Whatley J. C . White W. R. Winsbro Gale Young Cent ra l Research Library Document Reference Sec t ion GE Divis ion Library Laboratory Records Department Laboratory Records, ORNL R.C. ORNL Pa ten t Off ice

Externa l D i s t r i b u t i o n

9 3 . David E l i a s , USAEC, Divis ion of Reactor Development and Technol-

9 4 . Ralph H. Jones, USAEC, Divis ion of Reactor Development and Tech-

9 5 - 9 6 . T. W. McIntosh, USAEC, Divis ion of Reactor Development and Tech-

ogy, Washington, D. C . 20545.

nology, Washington, D. C. 20545.

nology, Washington, D. C . 20545.

158

97. M. Shaw, USAEC, Division of Reactor Development and Technology, Washington, D. C. 20545.

98-99. Division of Technical Information Extension.

100. Laboratory and University Division, USAEC, ORO.

W

ornl-tm-2815

Documents

f f i x

ion d i

i t s use

pages w i t h

r d i v

gummed stock i s

o f exit temperature

o f exit pressure